Question

1. what type of triangle is formed if the sides are a = 9, b = 12, and c = 15? a. scalene triangle b. acute triangle c. obtuse triangle d. right triangle

Explanation:

Step1: Apply Pythagorean theorem

Check if $a^{2}+b^{2}=c^{2}$.

Step2: Calculate $a^{2}+b^{2}$

$a = 9$, so $a^{2}=9^{2}=81$; $b = 12$, so $b^{2}=12^{2}=144$. Then $a^{2}+b^{2}=81 + 144=225$.

Step3: Calculate $c^{2}$

$c = 15$, so $c^{2}=15^{2}=225$.

Step4: Compare results

Since $a^{2}+b^{2}=c^{2}$, it is a right - triangle.

Answer:

d. Right triangle