Question

A rectangle has the same area as another, whose length is 6 m more and breadth
is 4 m less. It has also the same area as the third, whose length is 8 m more and
hreadth 5 m less. Find the length and breadth of the original rectangle.​

Answer 1

Answer:

Let the length and breadth of the original rectangle be x m and y m respectively.

According to the question,

Part 1--->

xy = (x+6)(y-4)

xy= xy + 6y - 4x - 24

4x - 6y = -24        ----eq.1

Part 2---->

xy = (x+8)(y-5)

xy = xy + 8y - 5x - 40

5x - 8y = -40       ----eq.2

Solving equation 1 and 2 by elimination method,

  20x - 30y = -120

- (20x - 32y = -160)

              2y = 40

y = 20  

Putting y's value in eq.1

4x - 6(20) = -24

x = 24

Therefore, the length and breadth of the original rectangle are 24 m and 20 m respectively.

Hope it helps..!!