Free Printable Pythagorean Theorem Problems

1.

What is the longest side of a right triangle called?

a)

Leg A

b)

Leg B

c)

Hypotenuse

d)

Pythagoras' Big Buddy

2.

A 25 foot ladder is leaning against a wall. The ladder is placed 10 feet away from the house. How far up the wall does the ladder reach?

Which diagram best represents the problem?

a)

b)

c)

d)

3.

The bottom of a 13-foot ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach? Which equation could be used to solve the problem?

a)

$5^2\ +\ 13^2\ =\ c^2$

b)

$a^2\ +\ 5^2\ =\ 13^2$

c)

$13^2\ +\ b^2\ =\ 5^2$

d)

$13^2\ -\ 5^2\ =\ c^2$

4.

If the two legs of a right triangle measure 8 inches and 12 inches, what is the length of the hypotenuse? Which equation could be used to solve the problem?

a)

$12^2\ +\ b^2\ =\ 8^2$

b)

$a^2\ +\ 8^2\ =\ 12^2$

c)

$8^2\ +\ 12^2\ =\ c^2$

d)

$12^2\ -\ 8^2\ =\ c^2$

5.

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide? Which equation could be used to solve the problem?

a)

$a^2\ +6^2\ =\ 8^2$

b)

$8^2\ +\ b^2\ =\ 6^2$

c)

$6^2\ +\ 8^2\ =\ c^2$

d)

$8^2\ -\ 6^2\ =\ c^2$

6.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across the field. How far do the players run? Which equation could be used to solve the problem?

a)

$120^2\ +\ 90^2\ =\ c^2$

b)

$a^2\ +\ 90^2\ =\ 120^2$

c)

$120^2-90^2\ =\ c^2$

d)

$120^2\ +\ b^2\ =\ 90^2$

7.

How far from the base of a house do you need to place a 15 foot ladder so that is exactly reaches the top of a 12 foot wall? Which equation could be used to solve the problem?

a)

$15^2\ -\ 12^2\ =\ c^2$

b)

$12^2\ +\ 15^2\ =\ c^2$

c)

$12^2\ +\ b^2\ =\ 15^2$

d)

12 + b = 15

8.

The diagonal of a rectangle is 25 inches. The width is 15 inches. Which equation could be used to solve the problem?

a)

$a^2\ +\ 15^2\ =\ 25^2$

b)

$15^2\ +\ 25^2\ =\ c^2$

c)

$a\ +\ 15\ =\ 25$

d)

$25^2\ +\ b^2\ =\ 15^2$

9.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be? Which equation could be used to solve the problem?

a)

$a^2\ +\ 10^2\ =\ 25^2$

b)

$25^2\ +\ 10^2\ =\ c^2$

c)

$25^2\ -\ 10^2\ =\ c^2$

d)

$25\ +\ 10\ =\ c^2$

10.

Jane and Miguel are siblings. They go to different schools. Jane walks 6 blocks east from home. Miguel walks 8 blocks north. How many blocks apart would the two schools be if you could walk straight from one school to the other? Which equation could be used to solve the problem?

a)

$8^2\ +\ b^2\ =\ 6^2$

b)

$8^2\ -\ 6^2\ =\ c^2$

c)

$a^2\ +\ 6^2\ =\ 8^2$

d)

$8^2\ +\ 6^2\ =\ c^2$

11.

A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew? Which equation could be used to solve the problem?

a)

$11^2\ +\ 8^2\ =\ c^2$

b)

$a^2\ +\ 8^2\ =\ 11^2$

c)

$11^2\ -\ 8^2\ =\ c^2$

d)

$11^2\ +\ b^2\ =\ 8^2$

12.

John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school? Which equation could be used to solve the problem?

a)

$6^2\ +\ 8^2\ =\ c^2$

b)

$a^2\ +\ 6^2\ =\ 8^2$

c)

$8^2\ +\ b^2\ =\ 6^2$

d)

$8^2\ -\ 6^2\ =\ c^2$

Pythagorean Theorem Problems

Total questions: 12

Worksheet time: 12mins

Similar Resources on Wayground