A building measuring 90m by 60m is to be built. A paved area of uniform width will surround the building. The paved area is to have an area of 9000m^2. How wide is the paved area
To find the width of the paved area, we need to subtract the total area of the building from the total area of the building with the paved area.
1. Calculate the total area of the building:
Area of the building = length × width
Area of the building = 90m × 60m
Area of the building = 5400m²
2. Calculate the total area of the building with the paved area:
Total area of the building with paved area = Area of the building + Area of the paved area
Total area of the building with paved area = 5400m² + 9000m²
Total area of the building with paved area = 14400m²
3. Find the width of the paved area:
Paved area = (length + 2 × width) × (width + 2 × width)
9000m² = (90m + 2 × width) × (60m + 2 × width)
9000m² = (90m + 2w)(60m + 2w)
9000m² = 5400m² + 300m²w + 120m²w + 4w²
0 = 1800m²w + 4w²
0 = 900m²w + 2w²
0 = w(900m² + 2w)
w = 0 or w = -900m²/2
Since width cannot be negative, we ignore the negative solution.
4. Solve for the width:
w(900m² + 2w) = 0
900m² + 2w = 0
2w = -900m²
w = -900m²/2
w = -450m²
Again, we ignore the negative solution. So the width of the paved area is 450m².
Therefore, the width of the paved area is 450 meters.
To find the width of the paved area, we can subtract the area of the building from the total area including the paved area.
1. First, calculate the area of the building.
The area of a rectangle is given by multiplying its length and width.
Thus, the area of the building = length × width = 90m × 60m = 5400m².
2. Next, calculate the total area including the paved area.
The total area = area of the building + area of the paved area.
Since we know that the total area is 9000m² and the area of the building is 5400m², the area of the paved area can be obtained by subtracting the area of the building from the total area.
Paved area = 9000m² - 5400m² = 3600m².
3. Finally, determine the width of the paved area.
The width of the paved area can be found by dividing the area of the paved area by the length of the building.
Width of the paved area = Paved area / length of the building = 3600m² / 90m = 40m.
Therefore, the width of the paved area is 40 meters.
(90 + 2w) * (60 + 2w) = (90 * 60) + 9000
4 w^2 + 300 w + 5400 = 5400 + 9000
w^2 + 75 w - 9000 = 0
(90+2w)(60+2w)=9000
(w+37.5)*2-2306.25=0
w=10.52m