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.

Answer and Explanation:

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.


Learn more about this topic:

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Measuring the Area of a Rectangle: Formula & Examples

from Geometry: High School

Chapter 8 / Lesson 7
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