SOLUTION: Hi I could really use some help with this question, I would really appreciate it. A square has a side of length 2x cm. In terms of x, what is its� a) perimeter? b) area?

Question 1083477: Hi I could really use some help with this question, I would really appreciate it.
A square has a side of length 2x cm. In terms of x, what is its�
a) perimeter?
b) area?

Thank you very much and have a good day
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the length of each side is 2x centimeters.

the perimeter of a square is equal to 4 times the length of each side.

the area of a square is equal to the length of each side squared.

therefore:

the perimeter is equal to 4 * (2x) = 8x

the area is equal to (2x)^2 which is equal to 2x * 2x which is equal to 4x^2

to see if this makes sense, let x = any number.

i chose 5.

we said earlier that the perimeter was equal to 4 * (2x).
when x = 5, the perimeter becomes equal to 4 * (2*5) which is equal to 4 * 10 which is equal to 40

we said earlier that the area was equal to (2x)^2.
when x = 5, the area becomes equal to (2*5)^2 which is equal to 10^2 which is equal to 100.

notice that (2x)^2 is not the same as 2x^2

(2x)^2 is equal to 2x * 2x which is equal to 2 * x * 2 * x which is equal to 2 * 2 * x * x which is equal to 4 * x^2 which is equal to 4x^2.

2x^2 is equal to 2 * x * x which is equal to 2 * x^2 which is equal to 2x^2.

big difference.

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