Question

what is the length of side x on the right triangle below? a $sqrt{34}$ b 4 c 8 d $sqrt{24}$

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Calculate the right - hand side

\(3^{2}=9\) and \(5^{2}=25\), then \(x^{2}=9 + 25=34\).

Step3: Solve for \(x\)

Taking the square root of both sides, \(x=\sqrt{34}\).

Answer:

A. \(\sqrt{34}\)