Chapter 8.2, Problem 7CYU

To determine

Whether the sides make a triangle or not.

The type of the triangle.

Answer to Problem 7CYU

Acute Triangle.

Explanation of Solution

Given:

The given sides are:

  $16,18,26$

Calculation:

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

  $\begin{array}{l}16+18>26\text{True}\\ 16+26>18\text{True}\\ 18+26>16\text{True}\end{array}$

According to Pythagorean Theorem,

  $\begin{array}{l}{\left(26\right)}^2\stackrel{?}{=}{\left(18\right)}^2+{\left(16\right)}^2\\ 676\stackrel{?}{=}324+256\\ 676>580\end{array}$

Hence, the given sides form anacute triangle.