Question

12 multiple choice 1 point
find the length of the leg. if your answer is not an integer, leave it in simplest radical form.
not drawn to scale
22
242
11√2
√11

Explanation:

Step1: Identify the triangle type

This is a \(45^{\circ}-45^{\circ}-90^{\circ}\) right - triangle. In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the hypotenuse \(c\) is related to the leg \(a\) (or \(b\)) by \(c = a\sqrt{2}\) (since \(a = b\)).

Step2: Solve for the leg length

Given \(c = 22\), and \(c=a\sqrt{2}\). Then \(a=\frac{c}{\sqrt{2}}\). Rationalize the denominator: \(a=\frac{22}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{22\sqrt{2}}{2}=11\sqrt{2}\).

Answer:

\(11\sqrt{2}\) (corresponding to the third option)