Question

the perimeter of a rectangle is 100m. If the length is decreased by 2m and the breadth is increased by 3m, then, area increased by 44m^2. Find the length and breadth of the rectangle?

Answer 1

Let the length and breadth of the rectangle be x and y respectively.
Area of rectangle = xy
Given when length inreased and breadth is reduced by 2m, the area is reduce by 28 sq m
Hence (x + 2)(y – 2) =  xy – 28
⇒ xy – 2x + 2y – 4 =  xy – 28
⇒ – 2x + 2y  =  – 28 + 4
⇒ – 2x + 2y  =  – 24
⇒  x – y  = 12 → (1)
It is also given that when length is reduced by 1m and breadth is increased by 2m, the area is increased by 33 sq m
Hence (x – 1)(y + 2) =  xy + 33
⇒ xy + 2x – y – 2 =  xy + 33
⇒ 2x – y =  33 + 2
⇒  2x – y  = 35 → (2)
Subtract (2) and (1), we get
    x – y  = 12
  2x – y  = 35
–     +      –   
----------------
– x = – 23
∴ x = 23
Put x = 23 in equation (1), we get
23 – y = 12
∴ y = 11
Thus length is 23 m and breadth is 11 m.

Answer 2

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