# A page of print containing 144 square centimeters of printed region has a margin of 4 and 1/2...

## Question:

A page of print containing 144 square centimeters of printed region has a margin of 4 and 1/2 centimeters at the top and bottom and a margin of 2 centimeters at the sides. What are the dimensions of the page if the width across the page is four units of the length?

## Rectangle:

We need to know the formula to calculate the area of a rectangle in order to solve this question. A rectangle with length l units and width w units has an area of {eq}l{\times}w {/eq} units.

Given: A page of print containing 144 square centimeters of the printed region has a margin of 4 and 1/2 centimeters at the top and bottom and a margin of 2 centimeters at the sides.

Let the width of the page be {eq}w {/eq} cm.

Let the length of the page be {eq}l {/eq} cm

Then, the length of the printed region is {eq}l-4-\frac{1}{2}=\frac{2l-9}{2} {/eq} cm.

The width of the printed region is

{eq}w-2-2=w-4 {/eq} cm.

As the width across the page is four units of the length,

{eq}l=4w {/eq}

The area of the printed region is

\begin{align} \frac{2l-9}{2}{\times}(w-4)=144 \\ \frac{2(4w)-9}{2}{\times}(w-4)=144 \\ (8w-9)(w-4)=288 \\ 8w^2-32w-9w+36=288 \\ 8w^2-41w-252=0 \\ \mbox{ Using the quadratic equation formula} \\ w=\frac{-(-41)\pm\sqrt{(-41)^2-4(8)(-252)}}{2(8)} \\ w=\frac{41\pm\sqrt{1681+8064}}{16} \\ w=\frac{41\pm\sqrt{9745}}{16} \\ w=\frac{41\pm98.72}{16} \\ \end{align}

we get the value of width as 8.73 and -3.61.

As the width cannot be negative.

The length is 34.92 cm and the width is 8.73 cm.

Hence, the dimension of the page is 34.92 by 8.73 units.