Chapter 8.2, Problem 6CYU

To determine

Whether the sides make a triangle or not.

The type of the triangle.

Answer to Problem 6CYU

Right Triangle.

Explanation of Solution

Given:

The given sides are:

  $15,36,39$

Calculation:

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

  $\begin{array}{l}15+36>39\text{True}\\ 36+39>15\text{True}\\ 15+39>36\text{True}\end{array}$

According to Pythagorean Theorem,

  $\begin{array}{l}{\left(39\right)}^2\stackrel{?}{=}{\left(36\right)}^2+{\left(15\right)}^2\\ 1521\stackrel{?}{=}1296+225\\ 1521=1521\end{array}$

Hence, the given sides form a right triangle.