Question

The length of a rectangle is 3 more than twice the breadth of a rectangle. If the length is reduced by 5 units and the breadth is increased by 3 units, the area remains the same. Find the dimensions of the original rectangle and also find the area

Answer 1

Let the original length and the breadth of the Rectangle be l and b respectively. 

   ∴ l = 3 + 2b   ---------eq(i). 

Area of the Rectangle = l × b

Now, If length is reduced by the 5 units and the breadth is increased by the 3 units, then area will be, 

  Area = (l - 5)(b + 3)

Now, Area in both the cases is same. 

∴ lb = (l - 5)(b + 3)

⇒ lb = lb + 3l - 5b - 15

⇒ 3l - 5b = 15

3(3 + 2b) - 5b = 15  [From eq(i)] 

9 + 6b - 5b = 15

b = 15 - 9

∴ b = 6 units. 

Thus, l = 3 + 2(6)

 l = 3 + 12

 l = 15 units.