Area Comparison: Square vs. Modified Rectangle with Side X cm

To determine which shape has a larger area, we need to compare the areas of the square and the rectangle:

• Step 1: Calculate the area of the original square:

The side length of the square is $X$, so its area is given by:

• Step 2: Calculate the area of the rectangle:

The dimensions of the rectangle are $X + 3$ cm and $X - 3$ cm. Thus, its area is:

Using the difference of squares formula, we find:

• Step 3: Compare the areas:

We compute the difference between the square's area and the rectangle's area:

Since 9 is positive, the area of the square is larger than the area of the rectangle.

Therefore, the square has a larger area than the rectangle.