Chapter 8.2, Problem 23PPS

To determine

Whether the sides make a triangle or not.

The type of the triangle.

Answer to Problem 23PPS

Yes

Right triangle.

Explanation of Solution

Given:

The given sides are:

  $4.5,20,20.5$

Calculation:

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

  $\begin{array}{l}20.5+4.5>20\text{True}\\ 4.5+20>20.5\text{True}\\ 20.5+20>4.5\text{True}\end{array}$

According to Pythagorean Theorem,

  $\begin{array}{l}{\left(20.5\right)}^2\stackrel{?}{=}{\left(4.5\right)}^2+{\left(20\right)}^2\\ 420.5\stackrel{?}{=}400+20.25\\ 420.5=420.5\end{array}$

Hence, the given sides form aright triangle.