Question

find d.
write your answer in simplest radical form.
inches

Explanation:

Step1: Identify Triangle Type

The triangle is a right - isosceles triangle (two angles are \(45^{\circ}\), one right angle), so the legs are equal. One leg is \(7\) in.

Step2: Use Pythagorean Theorem or 45 - 45 - 90 Triangle Ratio

For a 45 - 45 - 90 triangle, the hypotenuse \(d\) is related to the leg \(a\) by \(d=a\sqrt{2}\). Here, \(a = 7\) in. So \(d=7\sqrt{2}\) in.

Answer:

\(7\sqrt{2}\)