Question 1084316: A square lawn is bounded on three sides by a path 4 m wide if the area of the path is 7/8 that of the lawn find the dimensions of the lawn Answer by ikleyn(52781) (Show Source):
Let "x" be the unknown side of the lawn.
A square lawn surrounded on three sides by the path 4 m wide is a rectangle of dimensions (x + 2*4) = (x+8) and (x+4) meters.
The area of this rectangle is (x+8)*(x+4) m^2.
Then the area of the path is = = 12x + 32 m^2.
The condition says that
12x + 32 = .
It is
= 0.
Solve this quadratic equation for x.
Answer. x = 16 m.
