what equation represents the relationship of perimeter of a square varies directly as the length of it's side ?
P = 4s
Which equation represents the relationship between the side length, x, and the perimeter, y?
When the perimeter of a square varies directly with the length of its side, it means that if you double the length of the side, the perimeter will also double. Mathematically, we can express this relationship using a proportionality constant.
Let's denote the length of the side of the square as "s," and the perimeter as "P." Since the perimeter is directly proportional to the length of the side, we can write:
P ∝ s
To include the proportionality constant, we introduce a constant of proportionality, let's say "k." The equation can then be expressed as:
P = k * s
Now, to solve for the value of "k," we need to use a specific example. Let's take a square with a side length of 1 unit and calculate its perimeter. In this case, the perimeter is equal to four times the length of one side, so we have:
P = 4 * s
P = 4 * 1
P = 4
Now, we can substitute this value into our equation:
4 = k * 1
Since "k" represents the constant of proportionality, we can conclude that k = 4.
Hence, the equation representing the relationship of the perimeter of a square varying directly with the length of its side is:
P = 4s