Question

find y.
triangle with 45°, 45°, right angle, one leg 7√3 mm, hypotenuse y
write your answer in simplest radical form.
blank millimeters

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so the two legs are equal, and the hypotenuse is leg $\times\sqrt{2}$. The given side is a leg, $y$ is the hypotenuse.

Step2: Calculate hypotenuse $y$

Multiply the leg length by $\sqrt{2}$.
$y = 7\sqrt{3} \times \sqrt{2}$

Step3: Simplify the radical

Combine the square roots using $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$.
$y = 7\sqrt{3 \times 2} = 7\sqrt{6}$

Answer:

$7\sqrt{6}$ millimeters