Chapter 8, Problem 20SGR

To determine

Whether the given sides can be the sides of a triangle or not.

The type of the triangle formed.

Answer to Problem 20SGR

Yes.

Acute triangle.

Explanation of Solution

Given:

The given sides are:

  $65,72,88$

Calculation:

The sum of any two sides of a triangle must always be greater than the third side.

  $\begin{array}{l}65+72>88\\ 72+88>65\\ 65+88>72\end{array}$

Apply Pythagorean Inequality Theorem to check the type of the triangle,

  $\begin{array}{l}{c}^2=a^2+b^2\\ {88}^2\stackrel{?}{=}{65}^2+{72}^2\\ 7744\stackrel{?}{=}4225+5184\\ 7744<9409\end{array}$

Hence, the sides form an acute triangle.