What is the (width in feet) of a rectangular parking lot which covers 21,294 square feet and is 3 1/2 times as long as it is wide?
L = 7/2 W
a = L * W = 7/2 W^2
7/2 W^2 = 21294 ft^2
To find the width of the rectangular parking lot, we need to divide the area by the length.
Let's define the width of the parking lot as "w" in feet.
The length of the parking lot is given as 3 1/2 times the width, which can be written as 3.5w.
The area of the parking lot is given as 21,294 square feet. We can set up the equation:
w * 3.5w = 21,294
To simplify this equation, let's multiply the width and 3.5w:
3.5w^2 = 21,294
Dividing both sides of the equation by 3.5:
w^2 = 6,084
To solve for w, we will take the square root of both sides:
√(w^2) = √6,084
w ≈ 78
Therefore, the approximate width of the rectangular parking lot is 78 feet.
To find the width of the rectangular parking lot, we will need to divide the total area by its length, taking into account the given aspect ratio of 3 1/2.
Step 1: Determine the length of the parking lot
Since the parking lot's length is 3 1/2 times its width, we can set up the equation: length = (3 1/2) × width.
To simplify, we can convert the mixed number 3 1/2 to an improper fraction: 3 1/2 = (7/2).
Thus, the equation becomes: length = (7/2) × width.
Step 2: Calculate the area
The area of the parking lot is given as 21,294 square feet.
Step 3: Substitute the known values into the equation
Let's substitute the values into the equation to solve for the width:
21,294 (area) = length × width
21,294 = (7/2) × width
Step 4: Solve for the width
To isolate the width, we need to cancel out the fraction by multiplying both sides of the equation by 2:
(2 × 21,294) = (7/2) × width
42,588 = (7/2) × width
To further isolate the width, divide both sides of the equation by (7/2):
42,588 ÷ (7/2) = width
Now, perform the division:
42,588 × (2/7) = width
Step 5: Calculate the width
Multiply and divide to find the width:
width = (42,588 × 2) ÷ 7
width ≈ 12,168
Therefore, the width of the rectangular parking lot is approximately 12,168 feet.