Question

#3 two sides of a triangle measure 9 meters and 1 length of the third side if the side lengths are a pyth
a 13
b 14
c 15
d 16

Explanation:

Step1: Recall Pythagorean triples

Common Pythagorean triples include (3, 4, 5), (6, 8, 10), (5, 12, 13), (8, 15, 17), (7, 24, 25) etc. Also, if we consider the Pythagorean theorem $a^{2}+b^{2}=c^{2}$ for a right - triangle where $c$ is the hypotenuse. Given two sides 9 and 12.

Step2: Check with Pythagorean theorem

Let $a = 9$ and $b=12$. Then $a^{2}=9^{2}=81$ and $b^{2}=12^{2}=144$. So $a^{2}+b^{2}=81 + 144=225$. And $\sqrt{225}=15$.

Answer:

C. 15