Geometry · Practice

Pythagorean Theorem — Exercises

Graded practice problems from foundations to advanced. Enter your answer and press Check.

Foundations

Problem 1

A right triangle has legs $3$ and $4$ . Find the hypotenuse.

Problem 2

A right triangle has hypotenuse $13$ and one leg $5$ . Find the other leg.

Problem 3

A right triangle has legs $7$ and $24$ . Find $c^2$ .

Problem 4

A rectangle has width $3$ and height $4$ . Find the length of the diagonal.

Problem 5

Find the distance between points $(1, 2)$ and $(9, 8)$ .

Problem 6

A right triangle has legs $6$ and $8$ . Find the altitude to the hypotenuse.

Problem 7

Find the space diagonal of a box with dimensions $3 \times 4 \times 12$ .

Problem 8

A 30-60-90 triangle has hypotenuse $6$ . Find the shorter leg.

Problem 9

A square has diagonal $10$ . Find its area.

Problem 10

A right triangle has legs $10$ and $12$ . Find its area.

Problem 11

Find the shortest leg of a primitive Pythagorean triple with hypotenuse $25$ .