Question

The length of the rectangle is 2 more than 3 times its breadth, if both length and breadth are increased by 3 units, the new perimeter becomes 2 times the original perimeter. find the length and the breadth of the rectangle​

Answer 1

In this question,

Let

• Breadth of rectangle = x

Then, Length would be (2 + 3x) because length is 2 more than 3 times its breadth.

Perimeter of this rectangle = 2 (Length + Breadth)

⇒ Perimeter of original rectangle = 2 (2 + 3x + x)

⇒ Perimeter of original rectangle = 2 (2 + 4x)

⇒ Perimeter of original rectangle = (8x + 4) → → (Eqn. 1)

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When both length and breadth are increased by 3;

• Length = (2 + 3x) + 3 = 3x + 5
• Breadth = (x + 3)

Now let's find out the perimeter of rectangle when length and breadth are increased by 3.

Perimeter of new rectangle

= 2 (Length + Breadth)

= 2 (3x + 5 + x + 3)

= 2 (4x + 8)

= 8x + 16

⇒ Perimeter of new rectangle = (8x + 16) → → (Eqn.2)

According to the question,

Perimeter of new rectangle = 2 (Perimeter of old rectangle)

⇒ 8x + 16 = 2 (8x + 4)

⇒ 8x + 16 = 16x + 8

⇒ 16 - 8 = 16x - 8x

⇒ 8 = 8x

⇒ x = 1

Therefore,

• Breadth of rectangle = x = 1 unit
• Length = (2x + 3) = 2 + 3 = 5 units

∴ Breadth = 1 unit ; Length = 5 units