a square lawn is surrounded by a path of 2 5 m wide if the area of the - Maths - Perimeter and Area

Question

a square lawn is surrounded by a path of 2 5 m wide if the area
of the path is 165m2 find the area of the lawn ??

Petit Garcon · Accepted Answer

Let the side of the lawn be x
Since the width of the path = 2 5m
Side of the lawn including path = x + 2(2 5m) = x + 5m
So, area of lawn = (Area of the lawn inculding the path) - (Area
of the path)
We know that the area of a square = (side)^2
Therefore, we say :
x^2 = (x + 5)^2 - (165^m sq)
x^2 = (x^2 + 5x +5x +25) - (165m sq)
x^2 = x^2 + 10x + 25 - 165
x^2 = x^2 + 10x - 140
x^2 - 140 = x^2 - 10x (By transposing off)
x^2 - x^2 - 140 = -10x (By transposing off)
-140 = -10x
i e 140 = 10x
Therefore x = 140/10 = 14
Since the side of the lawn = 14m
The area of the lawn = (14)^2 or 196m sq

a square lawn is surrounded by a path of 2.5 m wide . if the area of the path is 165m2 find the area of the lawn ??