Chapter 9.3, Problem 8P

To determine

To find: The dimensions of the rectangle.

Answer to Problem 8P

The length is $25\text{cm}$ and width is $10\text{cm}$ .

Explanation of Solution

Given:

The length of a rectangle is $5\text{cm}$ less than three times is width and perimeter is $70\text{cm}$ .

Calculation:

Let the length is $l$ and width is $w$ .

From the given information,

  $l=3w-5$ …… (1)

And,

  $\begin{array}{c}2l+2w=70\\ l+w=35\end{array}$ …… (2)

Substitute $l=3w-5$ in equation (2).

  $\begin{array}{l}3w-5+w=35\\ 4w=35+5\\ 4w=40\\ w=10\text{cm}\end{array}$

Substitute $w=10$ in equation (1).

  $\begin{array}{c}l=3\left(10\right)-5\\ =30-5\\ =25\text{cm}\end{array}$

Therefore, the length is $25\text{cm}$ and width is $10\text{cm}$ .