Question

the length and breadth of a rectangle breath exceeds by 7 cm.if the length is decreased by 4 cm and the breadth is increased by 3cm,the area of the new rectangle is the same as the original rectangle.find the length and the breadth of the rectangle?

Answer 1

Naturally whatever is greater will be called length and the smaller one will be called breadth.
Let original and breadth be L and (L-7) ==> Area = L(L-7).
With new dimensions of length and breadth,
 length = (L-4) and breadth = (L-7) + 3 = (L- 4)
==> New area = (L-4)(L-4)  = original rectangular area = L(L-7)
 or L² - 8L +16 = L² - 7L  OR 8L - 7L = 16 ==> L = 16, 
==> length and breadth of original rectangle are 16 and 9 respectively.

Answer 2

let breadth=x
then length=x+7
area=l×b=x×x+7=x²+7x
length is  decreased by 4=x+3
breadth is increased by 3=x+3
area of new rectangle=x²+6x+9
x²+7x=x²+6x+9
x=9