Gallery of Pythagorean Theorem Problems
Enjoy our gallery of 24 customizable problems. A mixed up answer bank is provided at the end.
Substitute the names of friends to make the problems funny.

1.) was interviewing for a job as a financial advisor to a union of truck drivers These truck drivers drove frozen chicken parts all around the country, and they just didn't have the time to determine appropriate investment strategies. They needed a girl who was spunky and great with math.

said, "I'm your gal. I'll do a terrific job for you."

Henry, the head trucker was impressed with so he said, "Answer this one question correctly, and the job is yours. What 2 possible numbers, rounded to the nearest whole number, could complete this 'Pythagorean Triple'?
37, 25, _____ or _____

3.) is taking his SAT test in hopes of scoring high enough to get into the famous College of Modern Cheffery. Yes, he wants to be a Chef of the modern variety. He will be serving up kelp soup, soybean bread, and all kinds of organically responsible appetizers.

Here is the question the question bothering him at the moment. Find the length of the missing leg exactly.

5.) has a Pythagorean problem. You see he is planning a big bonfire,/campout on his pig farm.
He wants to invite Jenna, Kelly, Brittany, and Jessica as well as Luke, Jim, and Matt.

The problem is that the girls' parents won't let them attend unless they have their own tent. Well found an extra tent in his root cellar. It only has a little bit of mold on it, but it smells like old pig feet. He needs to get it set up and aired out before the party, but the support stick is missing. If the tent is 78 inches on the bottom and 42 inches on each side, to the nearest inch, how tall of a stick does he need to find?

7.) is in training for the great Appalachian Mid Winter Lake Swimming Contest. It takes place every February 15th. For extra warmth, contestants grease their naked bodies with a thick coat of chicken fat before putting on their swim suits. Then they jump into the freezing waters of lake Fingerfoo and swim their little hearts out. The winner gets $100 and an all you can eat dinner at Alice's Corn Pone Palace of Grits.

To train, swims across his pool diagonally every day. If his pool is 4 meters wide, and it's 16 meters diagonally across, how long is his pool to the nearest meter?

9.) is a famous math comedian for genius nerds. Her audiences have included gifted 14 year olds at MIT and Harvard, as well as an underground techno, hacker, club in downtown Cleveland.

One night a particularly odious twelve year old at the hacker club tried to hit on her. He said, "Hey hot mamma, you're obviously in need of my tangent to your curve. How would you affirm a union of our presently, mutually exclusive sets?"

To this replied, "I'll union my curve with your tangent if my age is less than or equal to yours. To find my age, find the hypotenuse on a right triangle to the nearest whole year, if its legs are SQRT(98) and SQRT(150).

11.) is a designer of portable computer screens. He is trying to design a computer screen that will fit in a woman's purse. That way she can have full computer functionality while on the go.

Imagine, she can design a web page or crunch numbers in a spreadsheet while in the ladies restroom at a restaurant.

His current design is 3/4 of a foot long and 1/2 foot wide. What will the EXACT measurement of the diagonal on this screen be. Leave your answer as a fraction in lowest,exact, terms.

13.) needs a miracle. You see she met this guy from Bosnia named Ahmed on the Internet. He sent her his picture, and he turned out to be a babe. Well to make a long story short, they kinda have a virtual thing going. His family is willing to pay her airfare so that she can go and visit him this summer.

Now dad doesn't want her to go, but he is afraid to make her mad, so he makes what he believes will be a no win deal. He tells her that she can go if she gets an 'A' in math the last quarter. Considering that has never gotten anything higher than a 'D' in the last three quarters, he feels it is a safe bet.

What her dad doesn't know is that Ahmed has been tutoring her in math over the Internet each evening. She is taking the last test of the year. She is on the last question. If she gets this one correct, she will have her 'A'. Here is the question.
Do the numbers 8, 10, 6 form a Pythagorean triple?

15.) designs playgrounds for little kids. He is doing one now in the shape of a right triangle. It needs to be skinny because it has to fit in a rat infested alleyway between two old buildings. The hypotenuse is 794 inches and the short leg is 156 inches. To the nearest inch, how much fencing does have to order to keep those rats out of the playground.

17.) is a disgruntled postal worker. She has simply had it up to her eyeballs with the stupid antics of the men in her mailroom. They are always doing things that she finds distasteful, like leaving rubber dog regurgitation on the lunch table right before she sits down, or passing around pictures of semi-clothed, voluptuous, females and drawing mustaches on them. They even have the nerve to visit "adult" Internet sites during their breaks when everyone knows that the computer is only to be used for tracking lost packages.

decides to play a trick of her own. No one in the mailroom knows that she is a math/computer whiz, so they'll never figure out it was her who did it. She puts a sophisticated entry password on the computer. The password is a question:

If two legs of a right triangle measure SQRT(90) and SQRT(40), what is the exact length of the hypotenuse.

19.) is a queen mud wrestler. She makes big bucks each evening slithering around in the mud and slamming the pretty faces of her opponents into the brown slimy goo. Usually everyone ends up laughing and having a good time no matter who wins. But wins most of the time.

Well last night she had a bit of a turnaround. She was wrestling a new woman from down south by the name of Big Bottom Bertha. Now Big Bottom pulled a move on that took her by surprise. She threw a handful of sand in eyes right as they rang the bell to start the match. Well this naturally blinded her, and she was then at the mercy of Big Bertha. The match was over almost as soon as it started.

The next morning when awoke, she couldn't see. She screamed in terror. Her eyes were all encrusted shut, and the pain was intense. Her mother rushed her to the hospital where their top opthamologist, Dr. , examined her eyes. He found 15 tiny rips on her cornea. The largest was in the shape of a right triangle.

If the two shorter sides were 0.025m and 0.01m, how long was the longest side to the nearest thousandth of a meter?

21.) runs the controls for a 20 foot tall, electronic Santa display. To keep old Kris Kringle anchored safely, he uses a 24 foot long steel cable attached to the top of Santa's head and bolted in a straight line to the floor. To the nearest tenth of a foot, how far away from Santa's feet is the cable?

23.) has worked her way up to the top ranks of "Who Wants to be a MILLIONAIRE?". She is on the million dollar round, and everyone in the nation is waiting to see if this little 15 year old from farm country, with the fantastic IQ, is going to break the bank.

She is so nervous that sweat drips from her eyebrows. Her mom and dad are in the audience as well has her boyfriend Marvin. Everyone else is watching from home. Here it comes,... the last question for ONE MILLION DOLLARS!

The hypotenuse of an isosceles, (2 legs the same length), right triangle is SQRT(50) units long. How long is each leg?

2.) had a bit of a problem. He was trying to make the moves on this cute chick in his study hall. She was in a grade lower, and she looked up to him as the dashing, OLDER, UPPERCLASSMAN that he was. She was almost afraid to talk to him for fear he would ignore her. Naturally, she thought he must know much more than her, because he was in a higher grade. So one day she got up enough nerve to ask him, "Can you help me with my math?"

was overjoyed. The hottie was speaking to him! "Sure," he said with confidence.

She smiled at him in a sexy manner and said,"GREAT! Here's the problem. Use the Pythagorean Theorem to find c, to the nearest tenth, if a=17 and b = 20."

Can do it? The future of his love life rests in the answer to a MATH problem.

4.) is training to be an Amazon Jungle tour guide. As part of her training, she must climb a slanted rope net into a tree that is 45 feet high. To the nearest hundredth of a foot, how far away from the tree does is the net anchored if the net is 100 feet long?

6.) works for the All Famous Flying Lizards Circus. He designs the ramps that the lizards run down in preparation for flight. He must be very precise in his measurements. Each lizard in the company has its own "ramp of flight" that has been designed for their body weight and length.

The circus just spent $3,000 to purchase the rare Komodo Dragon, Orange Speckled, Gecko lizard named Frank. Frank is 4 feet long and weighs 49.5 pounds. He will need a ramp 12.5 feet high with a base 20.923 feet long.To the nearest thousandth of a foot, how long will the ramp be.

8.) is a geometry teacher in an inner city school in Chicago. His classes just finished a unit on the Pythagorean Theorem. The test is tomorrow, and he is trying to review with the kids.

The class is all rowdy today. No one is paying attention. Every time tries to start a new problem, Jackson or Marcus, or Kyle pass gas or belch loud enough for the whole class to hear. This causes roars of laughter, and as a result, not much is being done.

pulls the three boys out into the hall and tells them that he is going to make a special test for them with only one question. Here it is:
Do the numbers, seventeen, the square root of twenty five, and sixteen form a Pythagorean Triple?

10.) Well good old is out on the sand dunes hang gliding again. She loves the feeling she gets when she is flying. It's like the whole world is a little toy beneath her.

She has her own glider. It was specially hand built and designed by a certain geometry teacher friend of hers in Chicago named . She calls it the TOYMAKER.

On her last flight she jumped off a cliff and traveled in a diagonal line for 500 feet before landing 450 feet from the base of the cliff. How high was the cliff to the nearest ten feet?

12.) is building a dollhouse for his mother's birthday. It has three floors and 12 rooms. He has been careful to use her favorite colors of powder pink and robin's egg blue.

He is ready to build the roof. Find the height of the roof to the nearest millionth of an inch if the house is 26 inches across and the slanted side is 15 inches long as shown below.

14.) is a famous artist. She has a reputation for producing beautiful murals. She likes to incorporate objects made of gold into each of her pieces as her distinct trademark.

The local retirement home has hired her to paint a mural of the four seasons. They have asked her to make it as cheerful and realistic as possible since some of the older folks can't get outside anymore.

She decides upon a 5 foot by 9 foot rectangle cut into four pieces by its two diagonals. She will use 24 Karat gold leaf tape for the diagonals so they glisten in the light and give a warm sunny feeling to the whole mural.

This tape is rather expensive though so she needs to know to the nearest tenth of a foot how much to buy for both diagonals.

16.) trains hamsters
to climb mole hills in the Lower Slewbobia Annual Rodent Olympics. Winners get medals and a year's supply of cedar chips.

has constructed a deluxe ramp for his hamster Dixon. The dimensions are drawn below. EXACTLY how high is the ramp?

18.) is in a burning building. She has her head out the window, and she is screaming at the top of her lungs while holding onto her pet Rotweiler Fuzzy.

The young, handsome, fireman, hears her cries and races to her rescue. He places a ten foot long ladder three feet away from the bottom of her building, and it reaches directly up to her window. He climbs up and reaches for . Fuzzy doesn't like this, and he lunges for fireman neck. He falls to the ground from the top of the ladder. How far does he fall to the nearest ten thousandth of a foot.

20.) is a mathematical genius, and he is sitting in an airport bored out of his mind. His flight has been delayed and he has already booked his luggage. The luggage had all of his reading material in it. He doesn't like the mindless magazines that are laying around the airport, and watching television is simply too much of an intellectual insult.

His eye however does catch an interesting poster hanging in the corner. The title reads, "AS THE CROW FLIES / YOUR GUIDE TO COMMON FLIGHT DISTANCES". He sees two cities which he knows are on the same longitude line, Slepport RI and Orange NJ. Now Las Vegas Nevada is directly 2,957 miles west of Orange and the flight distance from Slepport to Las Vegas is 3,000 miles.

sharp mathematical mind perceived a right triangle application. He mentally applied the Pythagorean Theorem and rounded the resulting square root to the nearest mile. This gave him the distance between Slepport and Orange. What did he get?

22.) designs Barbie Doll Accessories like cars and houses etc.. He is presently working on a Barbie Alpine Village set which includes a bridge across a raging river. The bridge design is below.

needs to find its total perimeter to determine how much plastic it will require. Find the perimeter to the nearest inch.

24.) is a digital diva. She works for the Sega company designing the play screens of some of the world's best selling video games.

To her the world is a coordinate grid system. Distance and length are always formulas taken from numbers on a grid.

She is working on the final scene of her latest game called. Shmelda Strikes Back. Shmelda is about to be destroyed by the ancient Icosmatron Queen. Shmelda must jump along the diagonal path of the rectangle with the coordinates below.

As you know if she overshoots the mark, she will fry. Find the length of the diagonal to the nearest tenth of a unit.

9.5394
8.9
220
no
24.373
SQRT(13)/4
506
13.3
7.483315
89.30
5
26.2
20.6
SQRT(8.75)
SQRT(17)
37
yes
0.027
16
16
SQRT(130)
27, 45
1729
15

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