Chapter 11.6, Problem 17WE

To determine

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

Answer to Problem 17WE

No.

Explanation of Solution

Given:

The sides of the triangle are $2a,3a,4a$ .

Calculation:

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

Let $a=2a,b=3a,c=4a$ . Then,

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

Thus,

  $\begin{array}{l}{c}^2=a^2+b^2\\ {\left(4a\right)}^2={\left(3a\right)}^2+{\left(2a\right)}^2\left\{\text{substitutes the given value}\right\}\\ 16a^2=9a^2+4a^2\\ 16a^2=13a^2\left\{false\text{statement}\right\}\end{array}$

Hence, the given side is not the side of the right-angle triangle.