A rectangular plot has a concrete path running in the middle of the plot parallel to the length of the plot. The rest of the plot is used as a lawn, which has an area of 2013 sq. m. if the width of the path is 4 m and the length of the plot is greater than its breadth by 8 m. what is the area of the plot? (in sq. metre)

Explanation:

Let the breadth of rectangular plot be x metre.

∴ Length = (x + 8) metre

∴ Area of path = (x + 8) × 4 sq. metre

∴ Area of lawn = x (x + 8) – (x+ 8) × 4

= (x + 8) (x – 4) sq. metre.

=> (x + 8) (x – 4) = 253

=> x^2+8x−4x−32=253

=> x^2+4x−285=0

=> x^2+19x−15x−285=0

=> x(x + 19) – 15 (x + 19) = 0

=> (x – 15) (x + 19)= 0

=> x = 15 because x = – 19

∴ Area of plot = (x + 8) × x

= (15 + 8) × 15

= 23 × 15 = 345 sq. metre.