Question

find c.
write your answer in simplest radical form.
centimeters

Explanation:

Step1: Identify triangle type

This is a 45-45-90 triangle, so legs are equal, hypotenuse \( h = leg \times \sqrt{2} \), or \( leg = \frac{hypotenuse}{\sqrt{2}} \). Here, hypotenuse is \( 6\sqrt{6} \), find leg \( c \).

Step2: Apply 45-45-90 ratio

\( c = \frac{6\sqrt{6}}{\sqrt{2}} \) (rationalize denominator: multiply numerator/denominator by \( \sqrt{2} \))
\( c = \frac{6\sqrt{6} \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{6\sqrt{12}}{2} \)
Simplify \( \sqrt{12} = 2\sqrt{3} \), so \( c = \frac{6 \times 2\sqrt{3}}{2} = 6\sqrt{3} \)

Answer:

\( 6\sqrt{3} \)