Question

use the relationships in 45-45-90 triangles to solve the following problem. if the hypotenuse of a triangle is 4 cm, what is the length of the leg? (1 point)
$2\sqrt{3}$ cm
2 cm
$4\sqrt{2}$ cm
$2\sqrt{2}$ cm

Explanation:

Step1: Recall 45-45-90 triangle ratios

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

Step2: Solve for leg length \( l \)

Given \( h = 4 \) cm, we rearrange the formula: \( l=\frac{h}{\sqrt{2}} \). Substitute \( h = 4 \): \( l=\frac{4}{\sqrt{2}} \). Rationalize the denominator: \( l=\frac{4\sqrt{2}}{2}=2\sqrt{2} \) cm.

Answer:

\( 2\sqrt{2} \) cm (the option with \( 2\sqrt{2} \) cm)