Question

the length of a rectangle exceeds the breadth by 6 m if the length is increased by 3 cm and the with declared by 2 cm the area remain the same find the length and breadth of a rectangle​

Answer 1

ANSWER:

Let the length of the rectangle be x+6

Let the breadth be x cm

Then according to the first statement,

the length of a rectangle exceeds the breadth by 6 m.

L = x+6

B = x

Area = ?

Area of the rectangle = L×B

Area of the rectangle = (x+6)(x)

Area of the rectangle = x^2+ 6x

Now, given that the length is increased by 3 cm.

So, now our length will be,

x + 6 + 3

And also stated that breadth is decreased by 2 cm,

So, now our bredth will be,

x - 2

We won't calculate the area with this new length and breath because according to the statement, the area remain the same.

So, our area is with this new length and breath too is x^2+ 6x

So, now let's move towards putting all these values and solving out and finding the length and breadth.

AREA OF THE RECTANGLE = L×B

x^2 + 6x =( x + 9 )( x - 2)

x^2 + 6x = x(x-2) + 9(x-2)

x^2 + 6x = x^2- 2x + 9x-18

x^2 -x^2 + 6x = 7x-18

6x = 7x-18

7x-6x = 18

x = 18

The value of x= the value of breadth

Breadth = 18 cm

Length = x+6

Length = 18 +6

Length = 24 cm.

Answer 2

Answer:

Step-by-step explanation:

Let x be the length then width will be x-6

when length increased by 3 cm then it will be x+3

and width decreased by 2 cm then it will be x+

x-6-2= x-8

and we know former area = new are.

so, x(x-6) = x+3(x-8)

x square -6x = x square -5x -24

x= 24

Length = 24

Width = 24-6= 18