Question

what is the length of the leg of a 45 - 45 - 90? * 1 point x $x\sqrt{2}$ $x\sqrt{3}$ 2x

Explanation:

Step1: Recall the properties of a 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the legs are of equal length. Let the length of each leg be \(a\), and the hypotenuse be \(c\). By the Pythagorean theorem \(a^{2}+a^{2}=c^{2}\), which simplifies to \(2a^{2}=c^{2}\) or \(c = a\sqrt{2}\). Here, if we assume the hypotenuse is \(x\sqrt{2}\), then the leg length \(a=x\).

Answer:

\(x\)