Question

find y. 18 yd write your answer in simplest radical form. yards

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the legs are equal and the hypotenuse \(c\) and leg \(a\) (or \(b\)) follow the relationship \(c = a\sqrt{2}\). Here, the hypotenuse \(c = 18\) yd, and we need to find the leg \(y\).

Step2: Use the 45 - 45 - 90 triangle formula

From \(c=a\sqrt{2}\), we can solve for \(a\) (where \(a = y\)). Rearranging gives \(y=\frac{c}{\sqrt{2}}\).
Substitute \(c = 18\) into the formula: \(y=\frac{18}{\sqrt{2}}\).
Rationalize the denominator: \(y=\frac{18\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{18\sqrt{2}}{2}=9\sqrt{2}\).

Answer:

\(9\sqrt{2}\) yards