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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 length of the parking lot is 15 yards and the width is 12 yards.

Step by step solution

01

Understanding the Problem

The area of the rectangle is given by the formula: Area = Length 脳 Width. According to the problem, the Length is 3 more than the Width. Let's denote the Width with \( w \), so the Length would be \( w + 3 \). It's also known that the area is 180 square yards.
02

Setting the Equation

Substitute these values of Length and Width into the formula of area, we get: \( w (w + 3) = 180 \). This is the equation we need to solve.
03

Solving the Equation

To solve the equation: \( w^2 + 3w - 180 = 0 \), you can use the quadratic formula \( w = \frac{-b \pm \sqrt{ b^{2} - 4ac}}{2a} \), where a = 1, b = 3 and c = -180. You get two solutions for w, w = 12 and w = -15. Ignore the negative result because width cannot be negative.
04

Calculating the Length

Now substitute the result of \( w = 12 \) into the equation for the Length (\(w + 3\)), to get the length equals 15.

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