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 $c = a\sqrt{2}$, then $a = \frac{c}{\sqrt{2}}$. in inches, what is the value of a?
○ 3
○ $3\sqrt{2}$
○ 6
○ $6\sqrt{2}$

Explanation:

Step1: Apply Pythagorean theorem

$a^2 + a^2 = 6^2$

Step2: Simplify left-hand side

$2a^2 = 36$

Step3: Isolate $a^2$

$a^2 = \frac{36}{2} = 18$

Step4: Solve for $a$

$a = \sqrt{18} = 3\sqrt{2}$

Answer:

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