Question

The perimeter of a rectangle is 100 metre if the length is decreased by 2 metre and the breadth is increased by 3 metre the area increases by 44 metre ^2 .Find the length and breadth of the rectangle.​

Answer 1

Step-by-step explanation:

Perimeter = 100

=>2 [ length + breadth ]=100

length + breadth = 100 / 2

length + breadth = 50

Let length be x m .

Breadth = ( 50 - x ) m

Area = x ( 50 - x ) m²

Now , new length = ( x - 2 ) m

And new breadth = ( 50 - x ) + 3

=> ( 53 - x ) m

New Area = ( x - 2 ) ( 53 - x ) m²

As per the condition ,

=>( x - 2 ) ( 53 - x ) - x ( 50 - x ) = 44

=>53 x - x² - 106 + 2 x - 50 x² = 44

=>5 x - 106 = 44

=>5 x = 106 + 44 = 150

=>x = 150 / 5

=>x = 30

Hence ,

The required length = 30 m

And breadth = 50 - 30

=> 20 m

hope it helps you....

Answer 2

Answer:

Let the length be l m and breadth be b m.

2( l + b) = 100

( l + b ) = 50

l = 50 - b

(l - 2) (b + 3) = lb + 4

lb + 3l - 2b - 6 = lb + 4

3l - 2b = 10

3(50 - b ) - 2b = 10

150 - 3b - 2b = 10

-5b = 10 - 150

5b = 140

b = 28

l = 50 - 28 = 22

Length of the rectangle = 22m.

Breadth of the rectangle = 28 m.