Chapter A.2, Problem 18AYU

To determine

Which are right triangles. For those that are, identify the hypotenuse.

Answer to Problem 18AYU

Right triangle; hypotenuse is 10.

Explanation of Solution

Given:

6, 8, 10

Calculation:

The triangle with sides of lengths 6, 8, and 10.

$6^2=36$

$8^2=64$

${10}^2=100$

Notice that the sum of the first two squares (36 and 64) equals the third square (100). That is, because $6^2+8^2={10}^2$, the triangle is a right triangle. The longest side, 10, is the hypotenuse.