Question

The length of a rectangle is increased by 3m
and breadth by 2 cm, the area will be increased
by 54cm², if the length is decreased by 2m
and breadth is increased by 2 m, then the
rectangle become a square find the length
and breadth of the rectangle,
​

Answer 1

Answer:

hxhbdbnxxjjdjjdhdjhdx

Answer 2

TO FIND -

The length and breadth of the rectangle.

ASSUMPTION -

Let us assume the length of the rectangle to be x centimetres and the breadth to be y metres.

FORMULA REQUIRED -

Area of rectangle = length × breadth

Here ,

length = x metres

breadth = y metres

Area of square = ( side )²

Here ,

side = x metres

SOLUTION -

According to the question, (rectangle)

length is increased by 3m = (x + 3) m

breadth is increased by 2m = y + 2 m

Area of the resulting rectangle = xy + 54 m²

Area of the resulting rectangle = l × b

xy + 54 = (x + 3) × (y + 2)

xy + 54 = xy + 2x + 3y + 6

xy - xy + 54 - 6 = 2x + 3y

48 = 2x + 3y

2x = 48 - 3y

x = 24 - 3/2y...eq(1)

According to the question, (square)

the length is decreased by 2m = (x - 2) metres

the breadth is increased by 2m = (y + 2) metres

then is becomes a square of area = (side)²

it becomes a square of side = (x - 2) or (y + 2)

Area of resulting square in terms of x = (side)²

= (x - 2)²

= x²+ 4 - 4x

Area of resulting square in terms of y = (side)²

= (y + 2)²

= y² + 4 + 4y

Therefore,

x² + 4 - 4x = y² + 4 + 4y

x² - y² = 4x + 4y

Putting eq(1) in instead of x² and then the equation becomes -