Question

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

Explanation:

Step1: Recall 45-45-90 triangle ratios

In a 45-45-90 triangle, the legs are equal, and the hypotenuse \( c \) is related to a leg \( l \) by \( c = l\sqrt{2} \).

Step2: Solve for the leg length

Given \( c = 18 \) cm, we solve \( 18 = l\sqrt{2} \) for \( l \). Divide both sides by \( \sqrt{2} \): \( l=\frac{18}{\sqrt{2}} \). Rationalize the denominator: \( l = \frac{18\sqrt{2}}{2}=9\sqrt{2} \) cm.

Answer:

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