Question

Describe the relationship between the area and the perimeter of two squares with a length of 2.5 and 5.

Answer 1

The perimeter and area are doubled. The small square is half of the bigger square

Answer 2

For this case we have by definition, that the area of a square is given by:

`A = l ^ 2`

While the perimeter is given by:

`p = 4l`

Where:

l: It's the side of the square.

Square 1:
`l = 2.5`

`A = (2.5) ^ 2 = 2.5 * 2.5 = 6.25\\p = 4 (2.5) = 10`

Square 2:
`l = 5`

`A = (5) ^ 2 = 5 * 5 = 25\\p = 4 (5) = 20`

We can see that the perimeter of the second square is double that of the first. In addition, the second area is four times that of the first square.

Answer:

`p_ {2} = 2p_ {1}\\A_(2) = 4A_ {1}`