Question

the hypotenuse of a 45°-45°-90° triangle measures 18 cm. what is the length of one leg of the triangle?
○ 9 cm
○ 9√2 cm
○ 18 cm
○ 18√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 leg length

Given hypotenuse \(h = 18\) cm, so \(x\sqrt{2}=18\). Solve for \(x\): \(x=\frac{18}{\sqrt{2}}\). Rationalize the denominator: \(x = \frac{18\sqrt{2}}{2}=9\sqrt{2}\) cm.

Answer:

\(9\sqrt{2}\) cm (corresponding to the option "9√2 cm")