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Pythagoras's Crazy Theorem Trivia Quiz

How much do you know about the theorem of Pythagoras? This quiz will involve questions about the theorem, determining side lengths, and will also have questions about Pythagorean Triples. All non-integral solutions will be in radical form.

A multiple-choice quiz by XxHarryxX. Estimated time: 4 mins.

Author
XxHarryxX

Time
4 mins

Type
Multiple Choice

Quiz #
204,916

Updated
Aug 13 24

# Qns
10

Difficulty
Average

Avg Score
7 / 10

Plays
4359

Last 3 plays: Guest 75 (7/10), Guest 97 (10/10), Guest 142 (10/10).

One at a Time - Single Page - Timed Game

Question 1 of 10

1. What is the formula for the Pythagorean Theorem? (^2 means squared) Hint

a^2 + b^2 = c

a + b = c^2

a^2 + b^2 = c^2

(a + b)^2

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Question 2 of 10

2. The right triangle is the only type of triangle the Pythagorean Theorem can be used on without being given any other measurements besides the sides (no height given).

True

False

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Question 3 of 10

3. If you have a right triangle with shorter side lengths a = 3 and b = 4; what will the hypotenuse, c, equal? Hint

none of these

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Question 4 of 10

4. If you have a right triangle with short side length a = 5 and hypotenuse length c = 13, what is the value of side length b? Hint

144

none of these

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Question 5 of 10

5. If you have a right triangle with side length b = 15 and hypotenuse length c = 17, what is the value of side length a? Hint

none of these

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Question 6 of 10

6. If you have a right triangle with shorter side lengths a = 7 and b = 12, what is the length of hypotenuse c? Hint

the square root of 19

none of these

the square root of 193

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Question 7 of 10

7. IF you have a right triangle with side length a = 3 and hypotenuse length c = 9, what is the value of side b? Hint

none of these

square root of 90

6 x (square root of 2)

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Question 8 of 10

8. The sets, 3,4,5; 5,12,13; and 8, 15, 17 are all examples of what? (The numbers are the side lengths of the triangles.) Please give your answer in plural form.

Answer: (Two Words, plural form)

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Question 9 of 10

9. I. 6-8-10 right triangle
II. 15-36-39 right triangle
III. 16-30-34 right triangle

Which one(s) is a true right triangle(s), meaning that they can work in the Pythagorean Theorem? Hint

III.

II.

all of them

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Question 10 of 10

10. Will a 99-132-165 right triangle's support the Pythagorean Theorem? (Meaning the sides can fit into the formula.)

Yes

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Most Recent Scores

Nov 19 2024 : Guest 75: 7/10
Nov 18 2024 : Guest 97: 10/10
Nov 06 2024 : Guest 142: 10/10
Oct 24 2024 : Guest 199: 9/10
Oct 08 2024 : Guest 174: 8/10
Oct 07 2024 : Guest 203: 1/10

Score Distribution

Quiz Answer Key and Fun Facts

1. What is the formula for the Pythagorean Theorem? (^2 means squared)

Answer: a^2 + b^2 = c^2

In the formula, a and b represent the shorter sides of a right triangle and the c represents the hypotenuse. Here's an example: You have shorter sides 3 and 4. What is the final side? Plug it into your equation: 3^2 + 4^2 = c^2. 9 + 16 = c^2. 25 = c^2. 5 = c.

2. The right triangle is the only type of triangle the Pythagorean Theorem can be used on without being given any other measurements besides the sides (no height given).

Answer: True

A right triangle is a triangle with a ninety degree angle in it. You have to have a height that is perpendicular to the base for the theorem to work, and a right triangle has the perpendicular height already. You can find the height of other triangles to make the Pythagorean Theorem work.

3. If you have a right triangle with shorter side lengths a = 3 and b = 4; what will the hypotenuse, c, equal?

Answer: 5

Plug it into your equation to solve it: 3^2 + 4^2 = c^2. Simplify to 9 + 16 = c^2, and add the 9 and 16 together to get 25 = c^2. Find the square root of both sides to get 5 = c. Your side lengths are 3, 4, and 5.

4. If you have a right triangle with short side length a = 5 and hypotenuse length c = 13, what is the value of side length b?

Answer: 12

Once again, plug the values into their appropriate spots: 5^2 + b^2 = 13^2. Simplify to 25 + b^2 = 169, and then subtract 25 from both sides to get b^2 = 144. Find the square root of both sides to get b = 12. Your side lengths are 5, 12, and 13.

5. If you have a right triangle with side length b = 15 and hypotenuse length c = 17, what is the value of side length a?

Answer: 8

Set up your equation: a^2 + 15^2 = 17^2. Simplify to a^2 + 225 = 289, and subtract 225 from both sides to get a^2 = 64. Find the square root of both sides and come up with your solution: a = 8. Your side lengths are 8, 15, and 17.

6. If you have a right triangle with shorter side lengths a = 7 and b = 12, what is the length of hypotenuse c?

Answer: the square root of 193

Plug those numbers into your formula: 7^2 + 12^2 = c^2. Simplify to 49 + 144 = c^2, and add your two terms together to get 193 = c^2. Find the square root of both sides to get c = square root of 193. 193 is prime, so you cannot simplify your answer any further because it does not have two like prime factors that can cancel each other out (like the square root of 2 times the square root of 2 equals 2). Your side lengths are 7, 12, and the square root of 193.

7. IF you have a right triangle with side length a = 3 and hypotenuse length c = 9, what is the value of side b?

Answer: 6 x (square root of 2)

Plug those numbers into your equation: 3^2 + b^2 = 9^2. Simplify to get 9 + b^2 = 81, then subtract 9 form both sides to get b^2 = 72. Take the square root of both sides to get b = square root of 72. Find the prime factorization of 72, which is 2 x 2 x 2 x 3 x 3. Notice you have two square root of 2's that can cancel to become a 2 and two square root of 3's that can cancel to give you 6 times the square root of 2. Your side lengths are 3, 6 x square toot of 2, and 9.

8. The sets, {3,4,5}; {5,12,13}; and {8, 15, 17} are all examples of what? (The numbers are the side lengths of the triangles.) Please give your answer in plural form.

Answer: right triangle

A Pythagorean Triple is a set of three integers that make the Pythagorean Theorem true. Multiples of Pythagorean Triples (like a 6-8-10 right triangle is a multiple of a 3-4-5 one because all the sides are multiplied by 2) will also prove the Pythagorean Theorem true.

9. I. 6-8-10 right triangle II. 15-36-39 right triangle III. 16-30-34 right triangle Which one(s) is a true right triangle(s), meaning that they can work in the Pythagorean Theorem?

Answer: all of them

They are all multiples of the three basic Pythagorean Triples. 6-8-10 is a multiple of 3-4-5, because all side lengths are multiplied by 2. 15-36-39 is a multiple of 5-12-13 because all side lengths are multiplied by 3. 16-30-34 is a multiple of 8-15-17 because all side lengths are multiplied by 2.

10. Will a 99-132-165 right triangle's support the Pythagorean Theorem? (Meaning the sides can fit into the formula.)

Answer: Yes

If you look closely, you will see that the sides are multiples of a 3-4-5 right triangle. They are all multiplied by 33. If you don't believe me, watch: 99^2 + 132^2 = 165^2. 9801 + 17424 = 27225. 27225 = 27225. I hope you have enjoyed my quiz and have learned something about the Pythagorean Theorem!

Source: Author XxHarryxX

This quiz was reviewed by FunTrivia editor crisw before going online.
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