Question

IB exams

The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?

Answer 1

let the breadth of the given rectangle be x then length is 2x. 
thus area of the given rect is 2x^2 


after dec 5cm from length and inc 5cm breadth 
new lenght becomes 2x-5 
and breadth is x+5 
thus new area =(2x-5)(x+5) 
=2x^2-5x+10x-25 
=2x^2+5x-25 
since new area is 75 units greater than original area thus 
2x^2+75=2x^2+5x-25 
5x=75+25 
5x=100 
therefore x=20 
hence length of the rectangle is 40 cm.

Answer 2

rectangle  length = L and  breadth = B.
       L = 2 B      and Area = LB = 2 B²

new length L' = L - 5 cm  = 2 B - 5  cm
new breadth  B' = B + 5 cm

New Area of rectangle = L'  B'
       = (2B - 5) (B + 5)
       =  2 B² + 10 B - 5 B  - 25

Increase in the  area =  L'B' - L B = 5 B - 25 
           = 75 cm²

   =>  B = (75+25)/5    =  20 cm
  =>     L = 2 B = 40 cm