Question

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.​

Answer 1

$\huge \underline \mathbb {SOLUTION:-}$

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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