Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X.

Question

What is the length, in centimeters, of one side of square Y?

Answer 1

Typical of SAT questions, there is a slow way of thinking through this, and a faster way.

The wording of the question prompts the reader to the slower way:

X's side is 12 centimeters, so its perimeter is 4 * 12 = 48.

Y's perimeter is twice X's, so 2 * 48 = 96.

Y's side length then is 96 / 4 = 24.

The faster way is to not be led into perimeter calculations, but to realize: for two squares, if the perimeter of Y is twice the perimeter of X, then the side length of Y is also twice the side length of X.

So Y's side length is 2 * 12 = 24; no additional calculation needed.

Answer 2

Let the side length of square X be s=12 cm.

By definition, the perimeter of a square is P=4s where s is the side length of the square.

Then we have P=4s=4(12)=48 cm and so the perimeter of square X is 48 cm.

Note that the perimeter of square Y is 2 times the perimeter of square X.

Observe that P=4s=48(2)=96 cm.

Thus 4s=96 produces s=24.

Therefore, the side length of square Y is 24 cm.

Answer 3

In a square, all sides are the same length. Squares have four sides, so the perimeter of square X can be represented by the following expression with units: (4)(12cm)

Square Y's perimeter is double that of square X, so it can be represented by this expression: (2)(4)(12cm)

When we simplify the expression, we get 96cm.

Since we only want one side, we can divide 96cm by 4 to get 24cm.

The length of one side of square Y is 24cm.

Answer 4