The length of a rectangle exceeds its breadth by 5m. If the width is increased by 1 m and the length is decreased by 2m the area of the new rectangle is 4 square metre less than the area of the original rectangle. Find the dimensions of the rectangle.

Problem : The length of a rectangle exceeds its breadth by 5m. If the width is increased by 1 m and the length is decreased by 2m the area of the new rectangle is 4 square metre less than the area of the original rectangle. Find the dimensions of the rectangle.

Doubt by Muskan

Solution : 

Let the breadth of the rectangle be x m
and the length of the rectangle be (x + 5) m.
Area of the rectangle = x (x + 5) m²

ATQ

(x + 1) (x + 5 - 2) = x (x + 5) - 4
(x + 1) (x + 3) = x² + 5x - 4
x ( x + 3) + 1 (x + 3) = x² + 5x - 4
x² + 3x + x + 3 = x² + 5x - 4
x² + 4x + 3 = x² + 5x - 4
4x + 3 = 5x - 4
3+4 = 5x - 4x
7 = x
x = 7

∴ Breadth of the Rectangle=x=7 m
   Length of the Rectangle=x+5=7+5=12 m