A square lawn is bounded on the three sides by a path of 4m wide.If the area of the path is 7/8 that of the lawn, find the dimensions of the lawn.

let the legth of the side of the square be x m
area of lawn = x²
area of the path path will be

=(x + 8)×4 + x×4 + x× 4

= 8x + 4x + 32

= 12x + 32
Given that area of the path is 7/8 that of the lawn

12x + 32 = (7/8)x²
so, 96x + 256 = 7x²
so, 7x² – 96x – 256 = 0
7x² – 112x + 16x – 256 = 0
7x(x – 16) + 16(x – 16) = 0
x = 16 m

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