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

Video Solution

Solution Steps

00:00 Mark the correct statement

00:03 Use the formula to calculate square area (side squared)

00:08 Use the formula to calculate square perimeter (4 times side)

00:16 Sum of perimeter and area

00:21 Add 4

00:33 Break down 4 into factors 2 and 2

00:39 Use shortened multiplication formulas to find the brackets

00:44 And this is the solution to the question

Step-by-Step Solution

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

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:

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

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