If the length of one side of a square is doubled, what happens to the area?

When the length of one side of a square is doubled, the effect on the area can be understood through the formula for the area of a square. The area ( A ) of a square is calculated as ( A = s^2 ), where ( s ) is the length of one side.

If the original side length is ( s ), the original area is ( A = s^2 ). When the side length is doubled, it becomes ( 2s ). The new area is calculated as follows:

[

A' = (2s)^2 = 4s^2

]

This means that the new area, ( A' ), is four times the original area ( A ):

[

A' = 4s^2 = 4A

]

Thus, doubling the length of one side of the square causes the area to increase by a factor of four, which means it quadruples. This is why the correct answer highlights that the area quadruples when the side length is doubled.