Question

If in a rectangle the length is increased and breadth is decreased by 2 units each, The area is reduced by 28 square units, if the length is reduced by 1 unit and breadth is increased by 2 units, the Area increased by 33 sq units. Find the dimensions of the rectangle

Answer 1

Let the original length of rectangle = X cm
The original breadth of rectangle = Y cm
Then area A = L x B cm^2

CASE 1.
Original length is increased by
2 units then new length = X + 2 cm
Original breadth is decreased by
2 units then new breadth = Y - 2 cm
The area is reduced by 28 square
units = A - 28 unit ^2

Therefore, A - 28 = (X + 2) (Y - 2)
A - 28 = XY - 2X + 2Y - 4
As XY = A
A - 28 = A - 2X + 2Y - 4
A - A - 28 + 4 = - 2X + 2Y
-24 = - 2X + 2Y
Divide it by 2
- 12 = - X + Y ................ (1)

CASE 2
Original length is decreased by
1 units then new length = X - 1 cm
Original breadth is increased by
2 units then new breadth = Y + 2 cm
The area is increased by 33 square
units = A - 33 unit ^2
Therefore, A - 33 = (X - 1) (Y + 2)
A + 33 = XY + 2X - Y - 2
As XY = A
A + 33 = A + 2X - Y - 2
A - A + 33 + 2 = 2X - Y
35 = 2X - Y ................ (2)

ADD (1) & (2)

( - 12 = - X + Y) + (35 = 2X - Y)
(- 12 + 35) = (- X + 2X) + (Y - Y)
23 = X
X = 23 cm
Replace X value in (2)
35 = [(2 x 23)] - Y
35 = 46 - Y
35 - 46 = - Y
- 11 = - Y
Y = 11 cm

*****Therefore, the original length is
23 cm and original breadth is 11 cm.