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°-45°-90° triangle.

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

Step2: Substitute the hypotenuse value.

Given \( c = 18 \) cm, substitute into the formula: \( a=\frac{18}{\sqrt{2}} \).

Step3: Rationalize the denominator.

Multiply numerator and denominator by \( \sqrt{2} \): \( a=\frac{18\sqrt{2}}{2}=9\sqrt{2} \) cm.

Answer:

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