Question

A rectangular plot of land is of dimension 28 by 18 it has a uniform path of uniform width running along its boundary or sides if area excluding the path is 264 m square find the width of the path

Answer 1

The width of the path is 3 m.

• The rectangular plot of land is 28 by 18. Therefore, length = 28 m and breadth = 18 m.

• Area of the rectangular plot = 28 × 18 = 504 sq. m

• There is a uniform width running around the boundaries of the field.

• Let the length of the width of the plot be x m.

• Therefore ,

Dimensions of the plot without the uniform path ,

Length = 28 - 2x

Breadth =  18 - 2x

• Area of the plot excluding the path is 264 sq. m

• Now,

(28 - 2x)(18 - 2x) = 264

504 - 36x -56x + 4x² = 264

4x² - 92x - 240 = 0

x² - 23x + 60 = 0

x² - 3x - 20x + 60 = 0

x (x - 3) - 20 (x - 3) = 0

(x-3)(x-20)=0

x = 3 or x = 20

But x cannot be equal to 20 as the width of the path cannot be greater than the breath of the rectangular plot.

∴ x = 3

• The width of the path is 3 m.