Chapter 11.6, Problem 14WE

To determine

To check: whether the three given number represents the lengths of the sides of the right triangle.

Answer to Problem 14WE

No.

Explanation of Solution

Given:

The sides of the triangle are $16\text{units},32\text{units},36\text{units}$ .

Calculation:

The given triangle is right angle tringle if and only if, it applies the Pythagoras theorem.

Let $a=16unit,b=32unit,c=36unit$ . Then,

, $c^2=a^2+b^2$

Thus,

  $\begin{array}{l}{c}^2=a^2+b^2\\ {36}^2={16}^2+{32}^2\left\{\text{substitutes the given value}\right\}\\ 1296=256+1024\{\because {16}^2=256,{32}^2=1024,{36}^2=1296\}\\ 1296=1280\left\{false\text{statement}\right\}\end{array}$

Hence, the given triangle is not the right angle triangle.