Question

1. challenge the length of the hypotenuse of an isosceles right triangle is 32 meters. find the length of the legs. round to the nearest tenth.

chapter 11 measurement and area

Explanation:

Step1: Recall the Pythagorean theorem for an isosceles right triangle.

Let the length of each leg be \( x \). In an isosceles right triangle, the legs are equal, and the hypotenuse \( c \) is related to the legs by \( c^2 = x^2 + x^2 = 2x^2 \). Given \( c = 32 \) meters, we substitute into the formula: \( 32^2 = 2x^2 \).

Step2: Solve for \( x^2 \).

First, calculate \( 32^2 = 1024 \). So, \( 1024 = 2x^2 \). Divide both sides by 2: \( x^2=\frac{1024}{2}=512 \).

Step3: Solve for \( x \).

Take the square root of both sides: \( x = \sqrt{512} \). Simplify \( \sqrt{512}=\sqrt{256\times2}=16\sqrt{2}\approx16\times1.414 = 22.624 \). Round to the nearest tenth: \( x\approx22.6 \).

Answer:

The length of each leg is approximately 22.6 meters.