Question

the length of a rectangle exceeds its breadth by 7 cm if the length is described by 4 cm and the breadth is increased by 3 cm the area of the new rectangle is the same as the original rectangle

Answer 1

let length be x
then, 
l = x ; b= x-7
arrea = x*x-7
         = x^2 - 7x
new length = x-4
new breath = x-7+3 = x-4
new area = (x-4)(x-4) = (x-4)^2 = x^2 + 16 - 8x
x^2 + 16 - 8x = x^2 -7x
x^2 - x^2 - 8x + 7x =  -16
- x = - 16
x = 16

Answer 2

When length was 7 more than its breadth,

let breadth = x  cm
     length    = (x + 7) cm


Area = length × breadth
         = x(x + 7)





When length is decreased by 4 cm and breadth is increased by 3 cm

length = (x + 7 - 4)cm = (x + 3) cm
breadth = (x + 3) cm


Area = length × breadth
         = (x + 3)(x + 3) 
         = (x + 3)^2  






Given that the Area remains same :


So,

x(x + 7) = (x + 3)^2 

x^2 + 7x = x^2 + 9 + 6x 

7x  =  9 + 6x 

7x - 6x = 9 

x=  9 





Hence, Breadth of original rectangle = x  = 9cm
             Length of original rectangle = (x+ 7) = 9+7 = 16 cm