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 \( \square \) yards.

To solve for the width, let's denote the width as \( w \) yards. Therefore, the length can be expressed as \( w + 9 \) yards. The area of a rectangle is given by the product of its length and width, which leads us to the equation: \[ w \cdot (w + 9) = 360 \] Expanding this, we have: \[ w^2 + 9w - 360 = 0 \] Now, using the quadratic formula, \( w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 9 \), and \( c = -360 \). Solving gives you the width as \( w = 15 \) yards, and the length as \( 24 \) yards! So, the parking lot has a width of 15 yards. For practical tips, remember that not all problems are neatly set up, so sketching can help visualize relationships like this. Also, keep in mind the properties of equations; don't neglect using properties of quadratic functions, as they can open many problem-solving doors! Did you know that many ancient civilizations had designated areas for parking their chariots? The concept dates back to the Romans, who created spaces along roadways specifically for carriages. Parking lots have transformed significantly since then, catering to various vehicles and accommodating the needs of urban development!