Chapter 8.2, Problem 22PPS

To determine

Whether the sides make a triangle or not.

The type of the triangle.

Answer to Problem 22PPS

Yes

Acute triangle.

Explanation of Solution

Given:

The given sides are:

  $10,12,23$

Calculation:

The sum of any two sides of triangle is greater than the third side.

  $\begin{array}{l}10+12>23\text{True}\\ 12+23>10\text{True}\\ 23+10>12\text{True}\end{array}$

According to Pythagorean Theorem,

  $\begin{array}{l}{\left(23\right)}^2\stackrel{?}{=}{\left(10\right)}^2+{\left(12\right)}^2\\ 529\stackrel{?}{=}100+144\\ 529>244\end{array}$

Hence, the given sides form an acute triangle.