Chapter 7.1, Problem 7P

To determine

To find: The dimensions of the triangle.

Answer to Problem 7P

The sides of the triangle are $\frac{9}{2}\text{cm,}\frac{15}{2}\text{cm,}3\text{cm}$ .

Explanation of Solution

Given:

The ratio of the three sides of the triangle are $3:5:6$ .

The perimeter of the rectangle is $21\text{cm}$ .

Calculation:

Consider the ratio of the dimensions is $3:5:6$ and the perimeter of the triangle is

Consider the perimeter of the triangle is,

  $P=a+b+c$

Then,

  $\begin{array}{l}21\text{cm}=3x+5x+6x\\ 14x=21\text{cm}\\ x=\frac{3}{2}\text{cm}\end{array}$

Then, the sides of the triangle are,

  $\begin{array}{l}3\left(\frac{3}{2}\text{cm}\right)=\frac{9}{2}\text{cm}\\ 5\left(\frac{3}{2}\text{cm}\right)=\frac{15}{2}\text{cm}\\ 3\left(\frac{6}{2}\text{cm}\right)=3\text{cm}\end{array}$