Question

the perimeter of rectangle is 100m if length is decreased by 2m and breath is increased by 3 m the area is increased by 44 m sq find length and breath

Answer 1

Hey mate..
========

Let, the length of the rectangle be x m And the breadth of the rectangle be y m

Given,

The perimeter of the rectangle is 100m

We know,

Perimeter of the rectangle = 2 ( L + B )

Thus,

2 ( x + y ) = 100

=> x + y = 50...(1)

Also,

If the length is decreased by 2m and breath is increased by 3 m the area is increased by 44 m

We know,

Area of the rectangle = L × B

So,

( x - 2 ) ( y + 3 ) = xy + 44

=> x ( y + 3 ) - 2 ( y + 3 ) = xy + 44

=> xy + 3x - 2y - 6 = xy + 44

=> xy - xy + 3x - 2y - 6 - 44 = 0

=> 3x - 2y = 50...(2)

Now,

We multiply Eq.(1) with 2 to get,

2x + 2y = 100...(3)

Thus,

Subtracting Eq.(2) from Eq.(3) We get,


=> ( 2x + 2y ) + ( 3x - 2y ) = 100 - 50

=> 2x + 2y + 3x - 2y = 50

=> 5x = 50

=> x = 50 / 5

•°• x = 10

Putting the value of x = 10 in Eq. (1) we get,

=> 10 + y = 50

=> y = 50 - 10

•°• y = 40

The required length of the rectangle is 10m

And the required breadth of the rectangle is 40m

Hope it helps !!