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 45-45-90 triangle ratios

In a \(45^\circ - 45^\circ - 90^\circ\) triangle, the ratio of leg : leg : hypotenuse is \(1:1:\sqrt{2}\). Let the length of each leg be \(x\), then hypotenuse \(h = x\sqrt{2}\).

Step2: Solve for \(x\)

Given \(h = 128\) cm, from \(h = x\sqrt{2}\), we get \(x=\frac{h}{\sqrt{2}}\). Substitute \(h = 128\):
\(x=\frac{128}{\sqrt{2}}\). Rationalize the denominator: \(x=\frac{128\sqrt{2}}{2}=64\sqrt{2}\) cm.

Answer:

\(64\sqrt{2}\) cm (corresponding to the option "64√2 cm")