Chapter A.2, Problem 6AYU

To determine

To fill: The triangle with sides of lengths 6, 8, and 10 is a right triangle.

Answer to Problem 6AYU

True.

Explanation of Solution

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

$6^2=36$

$8^2=64$

${10}^2=100$

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. Therefore statement is true.