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 the ratio of sides in a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle

In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the legs are of equal length and the hypotenuse \(c\) is related to a leg \(a\) by the formula \(c = a\sqrt{2}\).

Step2: Solve for the leg length \(a\)

Given \(c = 18\) cm. From \(c=a\sqrt{2}\), we can solve for \(a\) by \(a=\frac{c}{\sqrt{2}}\).
Rationalize the denominator: \(a=\frac{18}{\sqrt{2}}=\frac{18\sqrt{2}}{2}=9\sqrt{2}\) cm.

Answer:

B. \(9\sqrt{2}\) cm