Question

the length of a rectangle is 2 more than 3times it's breadth. if both length and breadth are increased by 3 the new perimeter becomes two times the present one. find the length and breadth of the rectangle.
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Answer 1

Answer:

The length of the rectangle = 5 units

and the breadth of the rectangle = 1 unit

Step-by-step explanation:

Given :

• The length of a rectangle is 2 more than 3 times it's breadth.
• If both length and breadth are increased by 3 the new perimeter becomes two times the present one.

To find :

the length and breadth of the rectangle

Solution :

Let the length of the rectangle be x units and it's breadth be y units.

⮞ The length of the rectangle is 2 more than 3 times it's breadth.

  x = 3y + 2

Perimeter of the rectangle :

Perimeter = 2(length + breadth)

➙ Perimeter = 2(x + y)

➙ Perimeter = 2(3y + 2 + y)

➙ Perimeter = 2(4y + 2)

➙ Perimeter = 8y + 4

⮞ Both length and breadth are increased by 3.

New length = x+3

New breadth = y+3

New perimeter of the rectangle :

Perimeter = 2(length + breadth)

➙ New Perimeter = 2(x+3 + y+3)

➙ New Perimeter = 2(3y + 2 + 3 + y + 3)

➙ New Perimeter = 2(4y + 8)

➙ New Perimeter = 8y + 16

⮞ New perimeter is two times the original perimeter.

8y + 16 = 2(8y + 4)

8y + 16 = 16y + 8

16y - 8y = 16 - 8

  8y = 8

   y = 8/8

  y = 1

⮞ Value of x :

x = 3y + 2

x = 3(1) + 2

x = 3 + 2

x = 5

Therefore, the length of the rectangle = 5 units

and the breadth of the rectangle = 1 unit

Answer 2

Step-by-step explanation:

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given,

1) length of a rectangle is 2 more than 3times it's breadth.

2) both length and breadth are increased by 3 the new perimeter becomes two times the present one.

solution:

let,

breadth of the rectangle be 'b'

length of the rectangle = 3b+2

perimeter of the rectangle = 2(l+b) = 2(b+3b+2)

= 2(4b+2) = 8b+4m

.: according to question,

for new perimeter =

breadth is increased by 3 = b+3

length is increased by 3 = 3b+2+3

= 3b+5

.: perimeter = 2(l+b) = 2(b+3+3b+5)

= 2(4b+8) = 8b+16

.: 8b+16 = 2(8b+4)

8b+16 = 16b+8

16-8 = 16b-8b

8b = 8

b = 1

.: breadth of rectangle = 1m

length of rectangle = 3(1)+2 = 5m