Chapter 7.1, Problem 66E

To determine

The dimensions of the rectangle.

Answer to Problem 66E

Length= $12$ centimetres

Width= $9$ centimetres

Explanation of Solution

Given information:

The perimeter is $42$ inches and the width is three-fourths the length.

Calculation:

To find the dimensions, start by letting $x$ stand for length and $\frac{3}{4}x$ stand for the width, while the perimeter equals $42$ . Plug these values into the standard perimeter formula.

  $\begin{array}{l}2(\text{width})+2(\text{length})=\text{Perimeter}\\ 2(\frac{3}{4}x)+2(x)=42\end{array}$

Now distribute and simplify to solve for $x$ :

  $\begin{array}{l}\frac{6}{4}x+2x=42\\ 3\frac{1}{2}x=42\\ x=12\end{array}$

Since, $x$ is $12$ that the length of the rectangle is $12$ inches. Since the width is three fourths the length and the width is $9$ inches.

  $\begin{array}{l}x=12\\ (\frac{3}{4})(12)=9\end{array}$

Thus, the length and width of the rectangle is $12$ and $9$ centimetres.