Problem 146 - College Algebra Essentials

Question

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.

Step-by-Step Solution

Answer

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

Step 1 Understanding the Problem

The area of the rectangle is given by the formula: Area = Length × 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.

Step 2 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.

Step 3 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.

Step 4 Calculating the Length

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