Question

x
√7
w
√17
3
v

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \( \triangle VWX\) with right - angle at \(W\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = VX=\sqrt{17}\), \(a = VW = 3\), and \(b=WX\). Let \(WX=x\), then \(x^{2}+3^{2}=(\sqrt{17})^{2}\).

Step2: Simplify the equation

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x>0\) (length of a side), \(x=\sqrt{8}=2\sqrt{2}\)

Answer:

\(2\sqrt{2}\)