Math Problem Statement
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. Question content area bottom Part 1 The parking lot has a width of enter your response here yards.
Solution
Let's denote the width of the parking lot as yards.
The length of the parking lot is 9 yards greater than the width, so the length is yards.
The area of the parking lot is given as 360 square yards, and the area of a rectangle is found using the formula:
Substituting the values we know:
Now, expand the equation:
Rearrange this into a standard quadratic equation:
We can solve this quadratic equation using the quadratic formula:
For the equation , the coefficients are:
Now substitute these values into the quadratic formula:
This gives two possible solutions:
or
Since the width cannot be negative, we take the positive solution:
Thus, the width of the parking lot is 15 yards.
Finding the length:
The length is 9 yards more than the width, so:
Final answer:
- Width: 15 yards
- Length: 24 yards
Would you like more details or have any questions?
Related Questions:
- How do you verify the area given the dimensions?
- What is the perimeter of the parking lot based on the dimensions?
- Can the quadratic formula be used in all such area-related problems?
- How would the solution change if the area was given in square meters instead of yards?
- What would happen if the width was greater than the length in this scenario?
Tip:
Always check the discriminant (the part inside the square root of the quadratic formula) to ensure it gives a real number solution before solving.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Geometry
Formulas
Area of a rectangle = length × width
Quadratic equation formula: ax^2 + bx + c = 0
Theorems
Quadratic Formula
Area Formula for Rectangles
Suitable Grade Level
Grades 8-10
Related Recommendation
Solve the Problem of Finding Length and Width of a Rectangle
Inequality for a Rectangular Parking Lot's Width Based on Area
Solve for Length and Width Using Quadratic Equations for a Rectangular Floor Area
Find the Length and Width of a Rectangular Parking Area
Solve Rectangle Dimensions Using Quadratic Equations