Question

If in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units. If, however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units. Find the area of the rectangle.

Answer 1

Answer : 253 square units

$\rule{100}2$

SolUtion :

Let length and breadth of rectangle be " p " & " q " respectively.

So, Area of rectangle = pq unit

⟿ It is given that,

when length increased and breadth reduced by 2 units, its area is reduced by 28 square units.

That is,

$\sf ( p + 2 ) ( q - 2 ) = pq - 28$

➵ $\sf {pq} - {2p} + {2q} -  4 = pq - 28$

➵ $\sf -2p + 2q = -28 + 4$

➵ $\sf -2p + 2q = - 24$

➵ $\sf p - q = 12$ ______________ ( ! )

In second part of ques, it is said that that when length is reduced by 1 unit and breadth increased by 2 units, the area increases by 33 square units.

That is,

➳ $\sf ( p - 1 ) ( q + 1 ) = pq + 33$

➳ $\sf pq + 2p - q - 2 = pq + 33$

➳ $\sf 2p-q = 33 + 2$

➳ $\sf 2p-q = 35$ ______________ ( !! )

subtract ( !! ) from ( ! )

we get,

p   -  q    =    12

2p  - q    =   35

( - )  ( + )      ( - )

⟶ - p = 23

∴ p = 23

Now,

substitute the value of ' p ' in ( ! ) to find the value of q.

we get,

23 - q = 12

➛  q = 11

∵ Area of rectangle = length × breadth.

$\sf = p\times q$

$\sf = 23\times 11$

$\sf = 253$

Hence,

Area of the given rectangle is 253 square units.

$\rule{200}2$