Question

x 5 3 4 5 \sqrt{17} \sqrt{21}

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 5\), \(b=3\), and \(a=x\). So \(x^{2}+3^{2}=5^{2}\).

Step2: Simplify the equation

\(x^{2}+9 = 25\). Then \(x^{2}=25 - 9\).

Step3: Calculate \(x^{2}\)

\(x^{2}=16\).

Step4: Solve for \(x\)

Take the square root of both sides. Since \(x>0\) (length), \(x=\sqrt{16}=4\).

Answer:

A. 4