Chapter 1.6, Problem 37E

Dimensions of a Lot A square plot of land has a building 60 ft long and 40 ft wide at one comer. The rest of the land outside the building forms a parking lot. If the parking lot has area 12,000 ft², what are the dimensions of the entire plot of land?

To determine

To find: The length and width of square plot.

Answer to Problem 37E

The length of garden is 60 ft and the width of garden is 40 ft.

Explanation of Solution

Given:

Length of building lot is 60 ft and width of building lot is 40 ft.

Area of the parking lot is $12,000{\text{ft}}^2$.

Calculation:

Let the side of square plot be x.

Tabulate the given information into the language of algebra.

In words	In Algebra
Side of square plot	x
Area of entire plot	$x^2$

Model the equation for the above information.

$\begin{array}{c}\text{Total}\text{area}\text{of}\text{plot}=\text{Area}\text{of}\text{building}\text{lot}+\text{Area}\text{of}\text{parking}\\ x^2=60\times 40+12000\end{array}$

Simplify the above equation for x,

$\begin{array}{c}{x}^2=2400+12000\\ x^2=14400\\ x=120\end{array}$

Thus, the side of square plot is 60 ft.