You are designing a parking lot for a business facility. The facility measures 110 feet long and 55 feet wide. By extending the length and width the same distance, you create a parking lot on 2 sides of the building. The area of the parking lot needs to be a total of 5850 feet. Find the distance added to the length and width of the building to accommodate the parking lot.
If I read this right, the parking lot extends the whole length and width of the building along its inside edges, meaning that the lot's area is
110x + 55x + x^2
So, now we solve
110x + 55x + x^2 = 5850
x = 30
To find the distance added to the length and width of the building, we need to determine the original area of the building and then subtract it from the desired total area of the parking lot.
Let's start by calculating the original area of the building, which is the length multiplied by the width:
Original Area = 110 ft × 55 ft
Next, we know that the parking lot is created by extending the length and width of the building on two sides. Thus, the new length will be L + x and the new width will be W + x, where x is the distance added to both sides.
The new area of the building, accommodating the parking lot, is then given by:
New Area = (L + x) × (W + x)
We are given that the total area of the parking lot needs to be 5850 square feet. Therefore, we can set up the equation:
New Area = Original Area + Total Area of Parking Lot
Substituting the values, we get the equation:
(L + x) × (W + x) = Original Area + 5850 ft²
Substituting the expressions for the original area and the new area, we now have:
(110 ft × 55 ft) + x^2 = (110 ft + x) × (55 ft + x)
Expanding the equation, we get:
6050 ft² + x^2 = 6050 ft² + 165 ft x + 110 ft x + x^2
Simplifying, we have:
165 ft x + 110 ft x = 0
Combining like terms, we obtain:
275 ft x = 0
Dividing both sides by 275 ft, we find:
x = 0
From the equation, we see that x is equal to zero, which implies that no distance needs to be added to the length and width of the building to accommodate the parking lot. Therefore, the parking lot is already designed to be on two sides of the building without any additional extension.