Question

a) $m = \frac{3\sqrt{2}}{4}$, $n = \frac{3\sqrt{2}}{4}$
b) $m = 3\sqrt{2}$, $n = 3\sqrt{2}$
c) $m = 3$, $n = 3$
d) $m = \frac{3\sqrt{2}}{2}$, $n = \frac{3\sqrt{2}}{2}$
\bigcirc a
\bigcirc b
\bigcirc c
\bigcirc d

Explanation:

Step1: Identify Triangle Type

The triangle is a right - isosceles triangle (one angle is \(45^{\circ}\), one is \(90^{\circ}\), so the third angle is also \(45^{\circ}\)). In a right - isosceles triangle, the legs are equal (\(m = n\)) and the hypotenuse \(h\) is related to the leg \(l\) by \(h=l\sqrt{2}\), or \(l=\frac{h}{\sqrt{2}}\).

Step2: Apply the Formula for Legs

Given the hypotenuse \(h = 3\). Using the formula \(l=\frac{h}{\sqrt{2}}\) (where \(l\) is the length of each leg, \(m\) and \(n\) in this case).

$$
LATEXBLOCK0
$$

Answer:

D) \(m = \frac{3\sqrt{2}}{2}\), \(n=\frac{3\sqrt{2}}{2}\)