The table shows the side lengths and perimeters of four squares.

Side Length (x)
Perimeter (y)
4.5
18
8.5
34
10.25
41
13.75
55

Which equation represents the relationship between the side length, x, and the perimeter, y?
y = one-fourth x
y = 4x
y = x + 13.5
y = x – 13.5

1 answer

To determine the equation that represents the relationship between the side length \(x\) and the perimeter \(y\) of squares, we can recall that the perimeter \(y\) of a square is calculated using the formula:

\[ y = 4x \]

where \(x\) is the side length.

Let's check the provided data with this formula to validate that this relationship holds:

  1. For \(x = 4.5\): \[ y = 4 \times 4.5 = 18 \]

  2. For \(x = 8.5\): \[ y = 4 \times 8.5 = 34 \]

  3. For \(x = 10.25\): \[ y = 4 \times 10.25 = 41 \]

  4. For \(x = 13.75\): \[ y = 4 \times 13.75 = 55 \]

Since all the calculated values for \(y\) match the given perimeters, the correct equation that represents the relationship between the side length \(x\) and the perimeter \(y\) is:

\[ y = 4x \]