Chapter 0, Problem 27PR

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 27PR

The triangle is not a right angle triangle.

Explanation of Solution

Given information:

  $a=12yd,b=14yd,c=16yd$

The diagram related to the given parameters is shown below,

  

Applying the Pythagoras theorem,

  $\begin{array}{c}{\left(12yd\right)}^2+{\left(14yd\right)}^2={\left(16yd\right)}^2\\ 144y{d}^2+196y{d}^2=256y{d}^2\\ 340y{d}^2\ne 256y{d}^2\end{array}$

So, it doesn’t satisfy Pythagoras theorem.

Therefore, the triangle is not a right angle triangle.