Question

The length of a rectangle exceeds the breadth by 5cm. If the length is decreased by 1cm and the breadth is increased by 3cm, then the area of the new rectangle increases by 32cm^2. Find the dimensions of the original rectangle.

Thanks!!

Answer 1

Let the breadth of original rectangle be x cm.
So, the length of the original rectangle is x+5 cm.
Area of original rectangle= l*b.
Therefore, Area= (x+5)x.
Length of the new rectangle= x+5-1 = 4+x cm.
Breadth of new rectangle= x+3 cm.
Area of new rectangle= Area of original rectangle+32cm².
i.e; (x+4)(x+3)= (x+5)x+32
x²+7x+12= x²+5x+32
7x-5x=32-12
2x=20
Therefore x=10.
So, the breadth of the original rectangle is 10cm and length is 15cm.