A rectangular building is to be built on a lot measuring 46m by 30m. The building will be surrounded by a strip of lawn of uniform width. If the lawn takes up 30% of the lot, how wide will the lawn be?
length = 46 + 2w
width = 30+2w
building area = (46-2w)(30-2w)
0.7 * lot area = building area
0.7*46*30 = (46-2w)(30-2w)
multiply it out and solve quadratic
To find the width of the lawn, we first need to calculate the area of the lot, and then the area of the lawn.
Step 1: Calculate the area of the lot
The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the lot is 46m and the width is 30m, so the area of the lot is:
Area of lot = length * width
Area of lot = 46m * 30m
Step 2: Calculate the area of the lawn
Since the lawn takes up 30% of the lot, we can find the area of the lawn by multiplying the area of the lot by 0.30 (which represents 30% as a decimal):
Area of lawn = Area of lot * 0.30
Step 3: Calculate the width of the lawn
To find the width of the lawn, we need to subtract the area of the lawn from the total area of the lot. Since the width is uniform (the same on all sides), we can divide the area of the lawn by the length (46m) to find the width:
Width of lawn = Area of lawn / Length
Let's calculate the width of the lawn using the given values:
Area of lot = 46m * 30m
Area of lawn = Area of lot * 0.30
Width of lawn = Area of lawn / Length
Substituting the known values into the formulas, we get:
Area of lot = 46m * 30m = 1380m²
Area of lawn = 1380m² * 0.30 = 414m²
Width of lawn = 414m² / 46m
Now, let's calculate the width of the lawn:
Width of lawn = 414m² / 46m ≈ 9m
Therefore, the width of the lawn will be approximately 9 meters.