Question

choose 1 answer: a (x = sqrt{60}) b (x = sqrt{119}) c (x = 13) d (x = 17)

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs of the right - triangle. Here, \(a = 5\), \(b = 12\), and \(x\) is the hypotenuse. So, \(x^{2}=5^{2}+12^{2}\).

Step2: Calculate the squares

\(5^{2}=25\) and \(12^{2}=144\). Then \(x^{2}=25 + 144\).

Step3: Add the values

\(25+144 = 169\), so \(x^{2}=169\).

Step4: Solve for \(x\)

Taking the square root of both sides, \(x=\sqrt{169}=13\) (we consider the positive value since \(x\) represents the length of a side of a triangle).

Answer:

C. \(x = 13\)