Question

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

a. right triangle
b. obtuse triangle
c. scalene triangle
d. acute triangle

Explanation:

Step1: Apply Pythagorean theorem

Check if $a^{2}+b^{2}=c^{2}$. Calculate $a^{2}=9^{2} = 81$, $b^{2}=12^{2}=144$, and $c^{2}=15^{2}=225$. Then $a^{2}+b^{2}=81 + 144=225=c^{2}$.

Step2: Determine triangle type

Since $a^{2}+b^{2}=c^{2}$, the triangle is a right - triangle. Also, since all side lengths ($9$, $12$, $15$) are different, it is a scalene triangle. A right - triangle is a more specific classification than a scalene triangle for this case.

Answer:

A. Right triangle