a square lawn 4m wide path surrounding it.if the area of the path is236m find the area of the lawn
To find the area of the lawn, we need to subtract the area of the path from the total area.
Let's assume the side length of the square lawn is x meters.
The width of the path surrounding the lawn is 4 meters, which means that the side length of the larger square (including the path) will be (x + 2*4) meters.
The area of the larger square (including the path) is (x + 2*4)^2 square meters.
The area of the smaller square (just the lawn area) is x^2 square meters.
The area of the path is the difference between the area of the larger square and the area of the lawn:
(x + 2*4)^2 - x^2 = 236
Expanding the equation:
(x + 8)^2 - x^2 = 236
Simplifying further:
x^2 + 16x + 64 - x^2 = 236
16x + 64 = 236
Subtracting 64 from both sides:
16x = 172
Dividing both sides by 16:
x = 10.75
Therefore, the side length of the lawn is approximately 10.75 meters.
The area of the lawn is x^2:
10.75^2 = 115.56 square meters.
So, the area of the lawn is approximately 115.56 square meters.
To find the area of the lawn, we'll need to subtract the area of the path from the total area including the path.
Let's say the side length of the square lawn is "x" meters.
The total area including the path can be calculated by adding the areas of the lawn and the path. The area of the lawn is simply x^2.
Now, let's determine the dimensions of the larger square that includes the lawn and the path. Since the path surrounds the lawn on all four sides, the side length of this larger square would be (x + 2*4) meters, as there is a 4-meter wide path on each side.
To find the area of the larger square, we square the side length:
(x + 2*4)^2
Expanding this expression, we get:
(x + 8)^2
Now, we can calculate the area of the path by subtracting the area of the lawn from the area of the larger square:
Area of Path = Area of Larger Square - Area of Lawn
236m^2 = (x + 8)^2 - x^2
Simplifying this equation, we get:
236m^2 = x^2 + 16x + 64 - x^2
Now, we can solve this equation to determine the value of "x".
16x + 64 = 236
Subtracting 64 from both sides:
16x = 172
Dividing both sides by 16:
x = 10.75
Now, we have determined the value of "x" which is the side length of the lawn.
To find the area of the lawn, we square x:
Area of Lawn = x^2
= (10.75)^2
= 115.56 m^2
Therefore, the area of the lawn is approximately 115.56 square meters.