A rectangular lawn is 60meters by 80meters. A part of the lawn is torn out to install a pool, leaving a strip of lawn of uniform width around the pool. The area of the poolnis 1/6 of the old lawn area. How wide is the strip of lawn?
To find the width of the strip of lawn, we first need to calculate the area of the old lawn and then determine the area of the pool.
The area of the old lawn can be calculated by multiplying the length by the width:
Area of old lawn = Length × Width
Given that the length of the rectangle is 60 meters and the width is 80 meters:
Area of old lawn = 60 meters × 80 meters = 4800 square meters
Now, we need to determine the area of the pool, which is 1/6 of the old lawn area:
Area of the pool = (1/6) × Area of old lawn
Substituting the value of the old lawn area:
Area of the pool = (1/6) × 4800 square meters = 800 square meters
The area of a rectangle can be calculated by multiplying the length by the width. In this case, we know the length and the area, so we can rearrange the formula to find the width:
Width of the pool = Area of the pool / Length of the pool
Width of the pool = 800 square meters / 60 meters = 13.33 meters (approximately)
Since the width of the pool is equal to the sum of the width of the strip of lawn on both sides, the width of the strip of lawn will be half of the width of the pool:
Width of the strip of lawn = 13.33 meters / 2 = 6.67 meters (approximately)
Therefore, the strip of lawn around the pool is approximately 6.67 meters wide.
If the strip has width w, the pool is
60-2w by 80-2w
So,
(60-2w)(80-2w) = 1/6 (60)(80)
Now just solve for w.