Question

the hypotenuse of a 45° - 45° - 90° triangle measures 22√2 units. what is the length of one leg of the triangle? 11 units 11√2 units 22 units 22√2 units

Explanation:

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

In a 45 - 45 - 90 triangle, if the length of the hypotenuse is \(c\) and the length of each leg is \(a\), then \(c = a\sqrt{2}\).

Step2: Solve for \(a\)

Given \(c=22\sqrt{2}\), from \(c = a\sqrt{2}\), we can solve for \(a\) by dividing both sides of the equation by \(\sqrt{2}\). So \(a=\frac{22\sqrt{2}}{\sqrt{2}}\).
Simplify \(\frac{22\sqrt{2}}{\sqrt{2}}\), the \(\sqrt{2}\) terms cancel out, and we get \(a = 22\).

Answer:

22 units