Chapter 11.6, Problem 18WE

To determine

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

Answer to Problem 18WE

Yes.

Explanation of Solution

Given:

The sides of the triangle are $3a,4a,5a$ .

Calculation:

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

Let $a=3a,b=4a,c=5a$ . Then,

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

Thus,

  $\begin{array}{l}{c}^2=a^2+b^2\\ {\left(5a\right)}^2={\left(3a\right)}^2+{\left(4a\right)}^2\left\{\text{substitutes the given value}\right\}\\ 25a^2=9a^2+16a^2\\ 25a^2=25a^2\left\{true\text{statement}\right\}\end{array}$

Hence, the given side is the side of the right-angle triangle.