A campground consist of 10 square campsites arranged in a line along the beach the distance from...

Question:

A campground consist of 10 square campsites arranged in a line along the beach the distance from the edge of the campsite to the water is 4 yards the area of the campground including the beach Is 1050 {eq}yd^2 {/eq}. what's the width of one campsite?

Rectangle:

A rectangle is a 2-dimensional figure, which has 4 sides. The pair of opposite sides of a rectangle are parallel to each other and are of the same length. The area of a rectangle with length l and width w is {eq}l{\times}w {/eq}

Answer and Explanation:

Let the width of one campsite be w yards.

The width of the campground will be 10w yards.

The length of the campground will be w yards.

The area of the campground is

$$\begin{align} A_1=w{\times}10w \\ A_1=10w^2 \end{align} $$

The width of the beach will be 10w yards.

The length of the beach will be 4 yards.

The area of the campground is

$$\begin{align} A_2=4{\times}10w \\ A_2=40w \end{align} $$

The total area is

$$\begin{align} A_1+A_2&=1050 \\ 10w^2+40w-1050&=0 \\ w^2+4w-105 &=0 \\ \mbox{ Using quadratic equation formula } \\ w&=\frac{-4\pm\sqrt{4^2-4(-105)}}{2} \\ w&=\frac{-4\pm\sqrt{16+420}}{2} \\ w&=\frac{-4\pm\sqrt{436}}{2} \\ w&=-2\pm\sqrt{109} \\ \end{align} $$

We get the value of w as -46.27 and 2.27 yards.

As width cannot be negative.

Hence, the width of one campsite is 2.27 yards.


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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