Question

a square plot has a 3 m wide path surrounding it. if the area of the path is 132 sq m. find the area of the plot.

Answer 1

Let the side of the square plot be x m
Let the side of the square plot including the path be x' m

x' can be calculated by adding width of the path

Thus, x' = x+3+3 m

 Let area of the square plot be A(1) and area of the square plot including the path be A(2)

Area can be calculated as,       A(1) = x*x   Meter Sqr
                             and               A(2) = x'*x' = (x+6)*(x+6)
                                                          = (x+6)^2
                                                          = x^2+36+12x

Area of path = Area of Square plot including path - Area of square plot
                     = A(2) -A(1)
                     =  x^2+36+12x - x^2
            132   = 36+12x
               12x = 132-36
                12x = 96
                    x = 8

Thus, area of the plot = x*x = 8*8 = 64 Meter Sqr

Answer 2

Let the side of the inner square measure Xm then its area will be X ×X=X^2

Since the path is 3m wide, then the side of the outer square =X+3+3=(X+6)m

Its area =(X+6) × (X+6)=X^2+12X+36

The area of the path =Area of outer square - Area of inner square =132m2

X^2 +12X +36-X^2=132m2

12X+36=132

12X=132-36

12X=96
X=8M

Length of the plot =8m

Area of the plot=8×8=64m2