Chapter A.2, Problem 22AYU

To determine

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

Answer to Problem 22AYU

Right triangle; hypotenuse is 26.

Explanation of Solution

Given:

10, 24, 26

Calculation:

The triangle with sides of lengths 10, 24, and 26.

${10}^2=100$

${24}^2=576$

${26}^2=676$

Notice that the sum of the first two squares (100 and 576) equals the third square (676). That is, because ${10}^2+{24}^2={26}^2$, the triangle is a right triangle. The longest side, 26, is the hypotenuse.