Question

choose 1 answer. a (x = sqrt{194}) b (x=sqrt{65}) c (x = 12) d (x = 10)

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(c = 13\), \(b = 5\), and we want to find \(a=x\). So \(x^{2}+5^{2}=13^{2}\).

Step2: Rearrange the equation

We get \(x^{2}=13^{2}-5^{2}\). Calculate \(13^{2}=169\) and \(5^{2}=25\). Then \(x^{2}=169 - 25\).

Step3: Calculate the value of \(x^{2}\)

\(x^{2}=144\).

Step4: Solve for \(x\)

Take the square - root of both sides. Since \(x\) represents the length of a side of a triangle, \(x>0\), so \(x = \sqrt{144}=12\).

Answer:

C. \(x = 12\)