Question

the hypotenuse of a 45°-45°-90° triangle measures 18 cm.
diagram of a 45°-45°-90° triangle with hypotenuse labeled 18 cm
what is the length of one leg of the triangle?
○ 9 cm
○ $9\sqrt{2}$ cm
○ 18 cm
○ $18\sqrt{2}$ 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 leg length be \(x\), hypotenuse \(h\). So \(h = x\sqrt{2}\).

Step2: Solve for \(x\)

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

Answer:

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