Question

If the length of a rectangle is increased by 2cm and breadth is reduced by 2cm,the area is reduced bu 28 cm.If the length is reduced by 1 cm and breadth is increased by 2 cm the area increased by 33 cm. Find the length and breadth of the rectangle.

Answer 1

Let the breadth be x and the length be y .

Original area =x.y

Now

length=y+2

breadth=x-2

Area=x.y-28 or x-2 × y+2

xy-28=(x-2)(y+2)

xy-28=xy+2x-2y-4

2y-2x=24

y-x=12

y=12+x

length=y-1

breadth=x+2

Area=xy+33 or (x+2)(y-1)

xy+33=(x+2)(y-1)

xy+33=xy-x+2y-2

35=2y-x

2y=35+x

y=(35+x)÷2

12+x=(35+x)÷2

24+2x=35+x

x=35-24

x=11

y=23

Therefore length is 23cm and breadth is 11cm.

Answer 2

Answer:

The breadth of the rectangle is 11 cm and length of the rectangle is 23 cm.

Step-by-step explanation:

The breadth of the rectangle is 11 cm and length of the rectangle is 23 cm.

Let The breadth be x cm and length be y cm.

Original area =xy square cm.

Now,the length of the rectangle is increased by 2cm and breadth is reduced by 2cm.

So,Length becomes y+2 cm.

Breath becomes x-2 cm.

So area (x-2)(y+2) square cm.

According to question,

$xy - 28 = (x - 2)(y + 2)$

$2y - 2x = 24$

$y - x = 12$

$y = 12 + x......(1)$

Again the length is reduced by 1 cm and breadth is increased by 2 cm.

So, length becomes (y-1) cm and breadth becomes (x+2) cm.

Therefore area is (x+2)(y-1) square cm.

According to question,

$xy + 33 = (x + 2)(y - 1)$

$2y = 35 - x$

$y = \frac{35 + x}{2} .......(2)$

From (1) and (2),

$12 + x = \frac{35 + x}{2}$

$12 + x = \frac{35 + x}{2}$

$x = 11$

From (1),

$y = 23$

So,breadth of the rectangle is 11 cm and length of the rectangle is 23 cm.