Solve for X: Square with Area 16 and Side Length (x+2)

To solve this problem, we'll follow these steps:

• Step 1: Set up the equation using the area of the square.
• Step 2: Solve for $x$ using algebraic methods.
• Step 3: Validate the solution against the given condition.

Now, let's work through each step:
Step 1: Given that the area of the square is 16, we use the area formula: $(x+2)^2 = 16$.
Step 2: Solving the equation, take the square root of both sides:
$x + 2 = \pm 4$ This produces two solutions: $x + 2 = 4 \quad \text{or} \quad x + 2 = -4$ Step 3: Solve each equation for $x$:
For $x + 2 = 4$, we have: $x = 4 - 2 = 2$ For $x + 2 = -4$, we have: $x = -4 - 2 = -6$ Since $x > -2$, we discard the solution $x = -6$ because it does not satisfy the condition.
Thus, the acceptable value is $x = 2$.

The length of the sides of the square is $x + 2 = 2 + 2 = 4$ cm.

Therefore, the solution to the problem is 4, and it matches with choice 1.