# The Pythagorean Theorem Exercises

### Example 1

Find *c* in the triangle shown below:

### Example 2

Find *x* in the triangle shown below:

### Example 3

How long is the hypotenuse of a right triangle with legs that have lengths 8 and 9?

### Example 4

A right triangle has a hypotenuse with a length of 13. One leg of the triangle is 3 times longer than the other leg of the triangle. How long are the legs of the triangle?

### Example 5

What does the Pythagorean Theorem say for a triangle with a hypotenuse of length *a* and legs of lengths *b* and *c*?