### Instruction: The numerical value of a particular square's area is equal to the numerical value of its perimeter. What is the length of a side of the square?### Response: I know that the area of a square is the length of a side squared, and the perimeter is four times the length of a side.
So I can write an equation that relates these two quantities.
Let x be the length of a side of the square.
Then the area is x^2 and the perimeter is 4x.
I want to find x such that x^2 = 4x.
I can simplify this equation by dividing both sides by x, as long as x is not zero.
This gives me x = 4.
However, I need to check if this is a valid solution, because I divided by x and I don't know if x is zero or not.
If x is zero, then the area and the perimeter are both zero, which is also a valid solution.
So there are two possible values for x: 0 or 4.
These correspond to two possible squares: one with no size at all, and one with a side length of 4 units.
I can verify that these squares have equal numerical values for their area and perimeter by plugging them into the formulas.
If x = 0, then the area is 0^2 = 0 and the perimeter is 4(0) = 0.
If x = 4, then the area is 4^2 = 16 and the perimeter is 4(4) = 16.
Therefore, the length of a side of the square can be either 0 or 4 units.