Question

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

Answer 1

Let the measure of each side of sq.lawn bex. Area of lawn =x^2. Area of path={(x+4)(x+8)} -x^2. Now acc.to ques: {(x+8)(x+4)} - x^2= (7/8)x^2. Solve it. You'll get:7x^2-96x-256=0. By mid term splitting you'll get:(7x+16)(x-16)=0. Thus, x=16 since measure of a side cannot be -ve.

Answer 2

Answer:

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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