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Chapter 1: Problem 146

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 the width of the parking lot be denoted by \( w \) (in yards), and the length be denoted by \( l \) (in yards). According to the problem we know that \( l = w + 3 \), and \( l \cdot w = 180 \)
02

Substitute and Solve

Substitute \( l = w + 3 \) into the equation for the area, \( l \cdot w = 180 \). This gives the equation \( (w + 3) \cdot w = 180 \), which simplifies to \( w^2 +3w -180 = 0 \). Solve this equation for \( w \). This equation is quadratic and can be factored to \( (w -12)(w + 15) = 0 \). So we get two roots \( w = 12 \) and \( w = -15 \)
03

Verify the Solution

The width can't be negative, so \( w = -15 \) is not acceptable. Therefore, the width of the parking lot \( w = 12 \) yards. Substitute \( w = 12 \) into \( l = w + 3 \), we get \( l = 12 + 3 = 15 \) yards.

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