Question

Triangle DEF is a right triangle with a right angle at vertex F. Side DF has a length of 9 inches and side FE has a length of 12 inches. What is the length, in inches, of side DE?

Answer 1

Answer:

$15$ inches.

Step-by-step explanation:

In a right triangle, the length of the hypotenuse can be found from that of the other two sides using the Pythagorean Theorem.

In this question:

• Side $({\rm DF}) = 9$ inches (adjacent to the right angle).
• Side $({\rm FE}) = 12$ inches (adjacent to the right angle).
• The length of side $({\rm DE})$ (hypotenuse, opposite the right angle) needs to be found.

By the Pythagorean Theorem:

$\begin{aligned} \underbrace{({\rm DE})}_{\text{hypotenuse}} &= \underbrace{\sqrt{({\rm DF})^{2} + ({\rm FE})^{2}}}_{\text{adjacent to right angle}} \\ &= \sqrt{9^{2} + 12^{2}} \\ &= 15 \end{aligned}$.

In other words, the length of the hypotenuse $({\rm DE})$ would be $15$ inches.