Question

the hypotenuse of a 45°-45°-90° triangle measures 128 cm.
what is the length of one leg of the triangle?
64 cm
64√2 cm
128 cm
128√2 cm

Explanation:

Step1: Recall the ratio of sides in a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle

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

Step2: Solve for \(a\) when \(c = 128\)

Given \(c=128\) and \(c = a\sqrt{2}\), we can solve for \(a\) by \(a=\frac{c}{\sqrt{2}}\). Rationalize the denominator: \(a=\frac{128}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{128\sqrt{2}}{2}=64\sqrt{2}\).

Answer:

\(64\sqrt{2}\text{ cm}\) (the second option)