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Chapter 0: Problem 32

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 12 yards and the length is 15 yards.

Step by step solution

01

Define the Variables

Let's define the width of the parking lot as \(w\) (in yards), and its length then would be \(w + 3\), as it's given that the length is 3 yards greater than the width.
02

Set up the Equation

Next, set up an equation based on the formula for the area of a rectangle (Area = length 脳 width). Using the given area of the parking lot, 180 square yards, the equation becomes \(w(w + 3) = 180\). This is a quadratic equation.
03

Solve the Quadratic Equation

Now, solve the equation. First simplify it: \(w^2 + 3w - 180 = 0\). Then solve for \(w\) using the quadratic formula or factoring. Factoring gives two potential solutions: \(w = 12, -15\). We dismiss \(w = -15\) since we can't have a negative width.
04

Find the Length

Finally, use the value of \(w = 12\) to find the length of the parking lot. Substituting \(w = 12\) into \(w + 3\), you get the length as 15 yards.

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