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Chapter 6: Problem 83

A rectangular parking lot has a length that is 3 yards greater than the width. The area of the parking lot is 180 square yards. Find the length and the width.

Short Answer

Expert verified
The width of the parking lot is 15 yards, and the length is 18 yards.

Step by step solution

01

Define the variables

Let's define \(x\) as the width of the parking lot. According to the problem, the length of the parking lot is 3 yards greater than the width. So, the length is \(x + 3\) yards.
02

Write the equation

The area of the parking lot is given as 180 square yards. Since the area of a rectangle is length x width, we can set up the equation: \(x(x + 3) = 180\).
03

Solve the equation

Rewrite the equation to the standard quadratic form \(ax^2 + bx + c = 0\): \[x^2 + 3x - 180 = 0\]. Factor the equation, \[(x - 15)(x + 12) = 0\] The possible solutions are \(x = 15\) and \(x = -12\). Since width cannot be negative, we only accept the positive solution, \(x = 15\).
04

Find the Length

Now, substitute \(x = 15\) into the equation for the length (\(x + 3\)) yielding \(15 + 3 = 18\). So, the length of the parking lot is 18 yards.

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Most popular questions from this chapter

As part of a landscaping project, you put in a flower bed measuring 10 feet by 12 feet. You plan to surround the bed with a uniform border of low-growing plants. a. Write a polynomial that describes the area of the uniform border that surrounds your flower bed. (Hint: The area of the border is the area of the large rectangle shown in the figure minus the area of the flower bed.) b. The low-growing plants surrounding the flower bed require 1 square foot each when mature. If you have 168 of these plants, how wide a strip around the flower bed should you prepare for the border?

Describe a strategy that can be used to factor polynomials.

What is factoring?

Use factoring to solve quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\)-intercepts. \((x-3)(x+8)=-30\)

In Exercises \(137-141,\) factor completely. $$(x+5)^{2}-20(x+5)+100$$
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