Question

find the value of x in the triangle shown below.

choose 1 answer:

a $x = \sqrt{60}$

b $x = \sqrt{119}$

c $x = 13$

d $x = 17$

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 5\), \(b=12\) and \(c=x\) (hypotenuse). So \(x^{2}=5^{2}+12^{2}\).

Step2: Calculate \(5^{2}+12^{2}\)

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

Step3: Simplify the right - hand side

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

Step4: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle (\(x>0\)), \(x=\sqrt{169}\), and \(\sqrt{169}=13\).

Answer:

C. \(x = 13\)