Question

below.
c.)

Explanation:

Step1: Identify Triangle Type

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

Step2: Find Length of \(v\) (and \(u\))

The hypotenuse is \(4\). Let the leg length be \(v\) (and \(u\), since legs are equal in \(45 - 45 - 90\) triangle). Using the formula \(l=\frac{h\sqrt{2}}{2}\), substitute \(h = 4\):
\(v=\frac{4\sqrt{2}}{2}=2\sqrt{2}\)
Since it's an isosceles right - triangle, \(u = v=2\sqrt{2}\)

Answer:

If we are finding \(v\) (or \(u\)), the value is \(2\sqrt{2}\)