Question

if a right triangle has sides 9 and 12, what is the length of the hypotenuse? a 18 b 17 c 15 d 16

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Let \(a = 9\) and \(b = 12\).

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}=9^{2}=81\), \(b^{2}=12^{2}=144\). Then \(a^{2}+b^{2}=81 + 144=225\).

Step3: Find the hypotenuse \(c\)

Since \(c^{2}=225\), then \(c=\sqrt{225}=15\).

Answer:

C. 15