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 property of a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle

In a \(45^{\circ}-45^{\circ}-90^{\circ}\) 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 \(c = 128\). From \(c=a\sqrt{2}\), we can solve for \(a\) by \(a=\frac{c}{\sqrt{2}}\). Substitute \(c = 128\) into the formula: \(a=\frac{128}{\sqrt{2}}\). Rationalize the denominator: \(a=\frac{128\sqrt{2}}{2}=64\sqrt{2}\).

Answer:

B. \(64\sqrt{2}\text{ cm}\)