Check the True Statement: Geometry Challenge with S = X² and P = 4X

Given a square of side length X

We will mark the area of the square by S and the perimeter of the square by P

Check the correct statement

To solve this problem, we begin by calculating the area and the perimeter of the square:

• Perimeter, $P = 4X$
• Area, $S = X^2$

The sum of $P$ and $S$ is:

$P + S = 4X + X^2$

We need to evaluate the choice that correctly equates:

Given the choice $P + S + 4 = (X + 2)^2$, we expand and simplify:

• $(X + 2)^2 = X^2 + 4X + 4$
• This expression matches $P + S + 4 = X^2 + 4X + 4$.

Thus, the expression $P + S + 4 = (X + 2)^2$ is correct.

Therefore, the solution to the problem is $P+S+4=(x+2)^2$.