Question

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

Explanation:

Step1: Identify triangle type

This is a 45-45-90 (isosceles right) triangle, so the legs are equal, and the hypotenuse $y$ is leg $\times \sqrt{2}$.

Step2: Substitute leg length

Leg length is $6\sqrt{3}$ cm. Calculate hypotenuse:
$y = 6\sqrt{3} \times \sqrt{2}$

Step3: Simplify the radical

Use $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$:
$y = 6\sqrt{3 \times 2} = 6\sqrt{6}$

Answer:

$6\sqrt{6}$ centimeters