Question

If the side of a square is tripled, how many times the perimeter of the first square will that of the new square be?

Answer 1

Let the length of each side of the old square = s

Then, perimeter of the old square = 4 × side = 4 × s = 4s

When the length of each side of the square is tripled, then

length of each side of the new square = 3s

∴ perimeter of the new square = 4 × side 

= 4 × 3s

= 3 × 4s

= 3 × perimeter of the old square    ...[∵ perimeter of the old square = 4s]

Hence, the perimeter of the new square will become three times the perimeter of the old square.

Answer 2

To determine how the perimeter of the new square compares to the original square when the side is tripled, follow these steps:

Step 1: Formula for the Perimeter of a Square

The perimeter of a square is given by:

P = 4 × Side

Step 2: Original Square

Let the side of the original square be s.

The perimeter of the original square:

P_old ​= 4 × s

Step 3: New Square (Tripled Side)

If the side of the square is tripled, the new side becomes 3s3s3s.
The perimeter of the new square:

P_new​ = 4 × (3s) = 12 × s

Step 4: Compare Perimeters

The ratio of the new perimeter to the old perimeter is:

`(P_"new")/(P_"old") = (12xxs)/(4xxs) = 3`

The perimeter of the new square will be 3 times the perimeter of the original square.