Question

The length of a rectangle is decreased by 3 and breadth is increased by 4.

The new area of the rectangle found after changing it's dimensions is same as

that of original rectangle before any changes were made. Which among below

is a correct equation? (Consider length of rectangle to be 'l' and breadth of

rectangle to be 'b’)

(a) 4l + 3b =12 (b) 3l -4b = 12 (c) 4l – 3b = 12 (d) 3l + 4b = 12​

Answer 1

Let the length & breadth of the original rectangle be x & y respectively. So its area will be xy

Now, the length of the rectangle is increased by 20% i.e. x2=x+20100x=x+15x=65x , & the breadth of the rectangle is decreased by 10% i.e. y2=y−10100y=y−110y=910y . Thus the area of the new rectangle will be x2y2=65x×910y=5450xy=2725xy

Thus, the area of the new rectangle will be 2725 times the area of the original rectangle.

Now let's calculate tge relative percentage increase in the area of the rectangle

A2−A1A1×100=2725xy−xyxy×100=225xyxy×100=225100=8

Thus, there is a total increase of 8% in the area of the original rectangle.

$hope \: \: \: it \: \: helps \: \: you.....$

Answer 2

Answer :

Option (c) 4l - 3b = 12

Step-by-step explanation :

Given :

• The length of a rectangle is decreased by 3 and breadth is increased by 4.

• The new area of the rectangle found after changing it's dimensions is same as  that of original rectangle.

To find :

the correct equation among the given options

Solution :

Let 'l' be the length of the rectangle and 'b' be the breadth of the rectangle.

First, let's find the area of the original rectangle.

➙ Area of the rectangle = length × breadth

➙ Area of the rectangle = l × b

➙ Area of the rectangle = lb

Now, changing the dimensions.

The length is decreased by 3

➙ New length, l' = l - 3

The breadth is increased by 4

➙ New breadth, b' = b + 4

Finding the area after changing dimensions.

➙ New area of the rectangle = l' × b'

➙ New area of the rectangle = (l - 3) (b + 4)

➙ New area of the rectangle = l(b + 4) - 3(b + 4)

➙ New area of the rectangle = lb + 4l - 3b - 12

As given,

Area of the original rectangle = New area of the rectangle

➙  lb = lb + 4l - 3b - 12

➙  4l - 3b - 12 = 0

➙  4l - 3b = 12

The required equation is 4l – 3b = 12