Question

find the length of side x in simplest radical form with a rational denominator.
triangle with 45°, 45°, right angle, hypotenuse 12, side x
answer attempt 1 out of 2
x = input box submit answer

Explanation:

Step1: Identify triangle type

This is a 45-45-90 triangle, so legs are equal, hypotenuse \( h = l\sqrt{2} \), where \( l \) is leg length.

Step2: Relate hypotenuse and leg

Given hypotenuse \( = 12 \), let leg \( = x \). So \( 12 = x\sqrt{2} \).

Step3: Solve for \( x \)

Divide both sides by \( \sqrt{2} \): \( x = \frac{12}{\sqrt{2}} \). Rationalize denominator: \( x = \frac{12\sqrt{2}}{2} = 6\sqrt{2} \).

Answer:

\( 6\sqrt{2} \)