Question

find the missing side length. all answers must be in radical form.
possible points: 10
8√2
45 45 90
x x x√2
2√8 2√16 8 8√2 16 16√2

Explanation:

Step1: Identify triangle type

This is a 45-45-90 triangle, so legs are equal (\(a = b\)) and hypotenuse \(= x\sqrt{2}\), where \(x\) is leg length.

Step2: Set up hypotenuse formula

Given hypotenuse \(= 8\sqrt{2}\), and hypotenuse formula for 45-45-90 is \(x\sqrt{2}\). Let leg length be \(x\), so:
\[
x\sqrt{2} = 8\sqrt{2}
\]

Step3: Solve for \(x\)

Divide both sides by \(\sqrt{2}\):
\[
x = \frac{8\sqrt{2}}{\sqrt{2}} = 8
\]
So \(a = b = 8\).

Answer:

\(8\) (and the legs \(a\) and \(b\) both have length \(8\))