Chapter 0, Problem 27PO

To determine

To evaluate: whether triangle is a right triangle in which the lengths of three sides of a triangle are given.

Answer to Problem 27PO

The triangle is not a right angle triangle.

Explanation of Solution

Given information:

  $a=6in,b=8in,c=12in$

The diagram related to the given parameters is shown below,

  

Applying the Pythagoras theorem,

  $\begin{array}{c}{\left(6in\right)}^2+{\left(8in\right)}^2={\left(12in\right)}^2\\ 36i{n}^2+64i{n}^2=144i{n}^2\\ 100i{n}^2\ne 144i{n}^2\end{array}$

So, it doesn’t satisfy Pythagoras theorem.

Therefore, the triangle is not a right angle triangle.