Chapter 8.2, Problem 25PPS

To determine

Whether the sides make a triangle or not.

The type of the triangle.

Answer to Problem 25PPS

Yes.

Obtuse triangle.

Explanation of Solution

Given:

The given sides are:

  $4.2,6.4,7.6$

Calculation:

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

  $\begin{array}{l}4.2+6.4>7.6\text{True}\\ 4.2+7.6>6.4\text{True}\\ 6.4+7.6>4.2\text{True}\end{array}$

According to Pythagorean Theorem,

  $\begin{array}{l}{\left(7.6\right)}^2\stackrel{?}{=}{\left(6.4\right)}^2+{\left(4.2\right)}^2\\ 57.56\stackrel{?}{=}40.96+17.64\\ 57.56<58.6\end{array}$

Hence, the given sides form anobtuse triangle.