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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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