Solve for X: Area vs. Perimeter in Two Altered Square Equations

Given two squares, one side of the squares is larger by 2 than the other. The area of the large square is larger than the perimeter of the small square by 20

Find the length of the small square

To find the length of the smaller square, we need to solve the equation derived from the problem statement:

• Step 1: Write down the equation for the area of the larger square: $(x + 2)^2$.
• Step 2: Write down the equation for the perimeter of the smaller square: $4x$.
• Step 3: Set up the equation as given: $(x + 2)^2 = 4x + 20$.

Let's solve the equation:

Step 1: Expand $(x + 2)^2$:

Step 2: Rewrite the equation substituting the expanded form:

Step 3: Simplify by eliminating $4x$ from both sides:

Step 4: Subtract 4 from both sides:

Step 5: Take the square root of both sides:

Since $x$ must be positive, we have:

Thus, the length of the side of the smaller square is $4$.