Chapter 8.2, Problem 21PPS

To determine

Whether the sides make a triangle or not.

The type of the triangle.

Answer to Problem 21PPS

Yes

Acute triangle.

Explanation of Solution

Given:

The given sides are:

  $7,15,21$

Calculation:

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

  $\begin{array}{l}7+15>21\text{True}\\ 7+21>15\text{True}\\ 15+21>7\text{True}\end{array}$

According to Pythagorean Theorem,

  $\begin{array}{l}{\left(21\right)}^2\stackrel{?}{=}{\left(15\right)}^2+{\left(7\right)}^2\\ 441\stackrel{?}{=}225+49\\ 441>274\end{array}$

Hence, the given sides form an acute triangle.