Question

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

Answer 1

Let the breadth be x cm

Therefore, length = (x + 7) cm.

Area = x ( x+ 7 ) sq. cm

Now,

length is decreased by 4 cm = x + 7 - 4

= x + 3 cm

Breadth = x + 3 cm

Area = ( x+3) ( x+3) sq. cm

ATQ,

( x+3) ( x+3) = x ( x+ 7 )

=> x^2 + 6x + 9 = x^2 + 7x

Cancelling x^2 and x^2

=> 6x +9 = 7x

=> 7x - 6x = 9

=> x = 9

Therefore,

breadth = x cm = 9cm

Length = ( x+7 ) cm = 9+7 = 16 cm.