Question

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 1

Let the side of the square lawn be x m.

Area of the square lawn = x² m²

The square lawn is bounded on three sides by a path which is 4 m wide.

Area of outer rectangle = (x + 4)(x + 8) = x² + 12x + 32

Area of path = x² + 12x + 32 – x² = 12x + 32

From the given information, we have:

`12x + 32 = 7/8 x^2`

`96x + 256 = 7x^2`

`7x^2 - 96x - 256 = 0`

`7x^2 - 112x + 16x - 256 = 0`

`7x(x - 16) + 16(7x + 16) = 0`

`(x - 16)(7x + 16) = 0`

`x = 16, (-16)/7`

Since, x cannot be negative.

So, x = 16 m.

Thus, each side of the square lawn is 16 m.