A rectangular parking lot has a length that is 9 yards greater than the width. The area of the parking lot is 360 square yards. Find the length and the width. The parking lot has a width of 15 yards. The parking lot has a length of \( \square \) yards.

To determine the length and width of the rectangular parking lot, let's follow the given information step by step. ### Given: - **Area of the parking lot:** 360 square yards - **Length is 9 yards greater than the width.** ### Let: - **Width = \( w \) yards** - **Length = \( w + 9 \) yards** ### Step 1: Set Up the Equation Using the Area Formula The area of a rectangle is calculated as: \[ \text{Area} = \text{Length} \times \text{Width} \] Plugging in the known values: \[ 360 = w \times (w + 9) \] \[ w(w + 9) = 360 \] ### Step 2: Expand and Formulate the Quadratic Equation \[ w^2 + 9w = 360 \] \[ w^2 + 9w - 360 = 0 \] ### Step 3: Solve the Quadratic Equation You can solve for \( w \) using the quadratic formula: \[ w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Where \( a = 1 \), \( b = 9 \), and \( c = -360 \). \[ w = \frac{-9 \pm \sqrt{9^2 - 4(1)(-360)}}{2(1)} \] \[ w = \frac{-9 \pm \sqrt{81 + 1440}}{2} \] \[ w = \frac{-9 \pm \sqrt{1521}}{2} \] \[ w = \frac{-9 \pm 39}{2} \] Since width can't be negative: \[ w = \frac{-9 + 39}{2} = \frac{30}{2} = 15 \text{ yards} \] ### Step 4: Find the Length \[ \text{Length} = w + 9 = 15 + 9 = 24 \text{ yards} \] ### **Final Answer:** - **Width:** 15 yards - **Length:** \( \boxed{24} \) yards