Question

what is the length of a leg of an isosceles right triangle whose hypotenuse measures 6 inches? let c represent the value of the hypotenuse. if the hypotenuse is c = a√2, then 6 = a√2. in inches, what is the value of a? 3, 3√2, 6, 6√2

Explanation:

Step1: Start with the given equation

We have the equation \( 6 = a\sqrt{2} \).

Step2: Solve for \( a \)

To isolate \( a \), divide both sides of the equation by \( \sqrt{2} \):
\( a=\frac{6}{\sqrt{2}} \)
Rationalize the denominator by multiplying the numerator and denominator by \( \sqrt{2} \):
\( a = \frac{6\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{6\sqrt{2}}{2}=3\sqrt{2} \)

Answer:

\( 3\sqrt{2} \) (corresponding to the option: \( 3\sqrt{2} \))