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

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

• A. The area remains the same
• B. The area doubles
• C. The area quadruples
• D. The area triples

Answer: (C)

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.

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.