Free Pythagorean Theorem Worksheet

Ten right-triangle problems using the Pythagorean theorem, with an answer key.

Answer key included

Name: Date:

The Pythagorean Theorem

A right triangle has a leg of

3

and a hypotenuse of

5

. Find the length of the other leg.

The legs of a right triangle measure

9

and

12

. Find the length of the hypotenuse.

A right triangle has a leg of

8

and a hypotenuse of

17

. Find the length of the other leg.

The legs of a right triangle measure

7

and

24

. Find the length of the hypotenuse.

The legs of a right triangle measure

8

and

15

. Find the length of the hypotenuse.

A right triangle has a leg of

36

and a hypotenuse of

60

. Find the length of the other leg.

A right triangle has a leg of

40

and a hypotenuse of

58

. Find the length of the other leg.

A right triangle has a leg of

27

and a hypotenuse of

123

. Find the length of the other leg.

The legs of a right triangle measure

3

and

4

. Find the length of the hypotenuse.

10.

The legs of a right triangle measure

9

and

40

. Find the length of the hypotenuse.

Name: Answer KeyDate:

The Pythagorean Theorem

A right triangle has a leg of

3

and a hypotenuse of

5

. Find the length of the other leg.

Answer:

4

The legs of a right triangle measure

9

and

12

. Find the length of the hypotenuse.

Answer:

15

A right triangle has a leg of

8

and a hypotenuse of

17

. Find the length of the other leg.

Answer:

15

The legs of a right triangle measure

7

and

24

. Find the length of the hypotenuse.

Answer:

25

The legs of a right triangle measure

8

and

15

. Find the length of the hypotenuse.

Answer:

17

A right triangle has a leg of

36

and a hypotenuse of

60

. Find the length of the other leg.

Answer:

48

A right triangle has a leg of

40

and a hypotenuse of

58

. Find the length of the other leg.

Answer:

42

A right triangle has a leg of

27

and a hypotenuse of

123

. Find the length of the other leg.

Answer:

120

The legs of a right triangle measure

3

and

4

. Find the length of the hypotenuse.

Answer:

5

10.

The legs of a right triangle measure

9

and

40

. Find the length of the hypotenuse.

Answer:

41

Scroll to see all 10 problems and the answer key on its own page. Printing includes every page.

About this worksheet

Given the two legs, students find the hypotenuse — the theorem in its cleanest form. Many problems use Pythagorean triples so answers come out whole, letting students focus on the setup a² + b² = c² instead of decimal wrangling.

Students shaky on the skill itself? Send them to the free lesson: The Pythagorean Theorem — explained step by step.

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Free Pythagorean Theorem Worksheet

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