Question

can the sides of a triangle have lengths of 27, 36, and 45? if so, what kind of triangle is it? yes, acute yes, right yes, obtuse no

Explanation:

Step1: Check triangle - inequality

The sum of any two sides of a triangle must be greater than the third side.
$27 + 36=63>45$, $27 + 45 = 72>36$, $36 + 45=81>27$. So, a triangle can be formed.

Step2: Determine the type of triangle

Use the Pythagorean - theorem $a^{2}+b^{2}=c^{2}$ (for right - triangle), $a^{2}+b^{2}>c^{2}$ (for acute - triangle), $a^{2}+b^{2}Calculate $27^{2}+36^{2}=729 + 1296=2025$, and $45^{2}=2025$.
Since $27^{2}+36^{2}=45^{2}$, the triangle is a right - triangle.

Answer:

yes, right