A rectangular parking lot has a length that is

99

yards greater than the width. The area of the parking lot is

360360

square yards. Find the length and the width.

Question content area bottom

Part 1

The parking lot has a width of

enter your response here

yards.

To solve for the width and length of the parking lot, let's denote the width as \( w \) yards. According to the problem, the length of the parking lot is 99 yards greater than the width, so the length can be expressed as \( w + 99 \) yards.

The area of the parking lot is given as 360,360 square yards. The area of a rectangle is calculated by multiplying the length by the width, so we have the equation:

\[
\text{Area} = \text{Length} \times \text{Width}
\]
\[
360360 = (w + 99) \times w
\]

This expands to the quadratic equation:

\[
w^2 + 99w - 360360 = 0
\]

We can solve this quadratic equation using the quadratic formula:

\[
w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, \( a = 1 \), \( b = 99 \), and \( c = -360360 \). Let's calculate the value of \( w \).The solutions to the quadratic equation are approximately \( w_1 = 552.84 \) yards and \( w_2 = -651.84 \) yards. 

Since the width cannot be negative, the width of the parking lot is approximately **552.84 yards**.

Would you like the details on how to calculate the length, or do you have any other questions?

### Follow-up Questions:
1. What is the exact length of the parking lot based on this width?
2. How do you derive the quadratic formula from a general quadratic equation?
3. What happens if the area of the parking lot were different, say 500,000 square yards?
4. How would the problem change if the length were 50 yards greater instead of 99 yards?
5. What if the width was known, how would you find the length?
6. How can you verify that the width we found is correct?
7. Could there be any other methods to solve this problem?
8. What would the equation look like if the parking lot were a square?

### Tip:
When solving quadratic equations, always consider both potential solutions, but remember that only physically meaningful (e.g., positive) solutions apply in real-world problems.

Learn how to find the length and width of a rectangular parking lot given its area and the relationship between length and width. This problem involves quadratic equations and is suitable for students in Grades 7-9.

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