To solve this problem, we need to find the equation that represents the side length [tex]\( x \)[/tex] of the greater square created from a 10 by 10 grid.
First, calculate the total area of the 10 by 10 grid:
[tex]\[ \text{Total area} = 10 \times 10 = 100 \][/tex]
Next, let's denote [tex]\( x \)[/tex] as the side length of the greater square. According to the problem, the side length of the smaller square is 2 units less than that of the greater square, so the side length of the smaller square is [tex]\( x - 2 \)[/tex].
Now let's write the equations for the areas of the two squares:
- The area of the greater square is [tex]\( x^2 \)[/tex].
- The area of the smaller square is [tex]\( (x - 2)^2 \)[/tex].
Since the two squares must use all of the area from the 10 by 10 grid, their combined areas should equal the total area of the grid:
[tex]\[ x^2 + (x - 2)^2 = 100 \][/tex]
Thus, the equation that represents [tex]\( x \)[/tex], the side length of the greater square, is:
[tex]\[ x^2 + (x - 2)^2 = 100 \][/tex]
So, the correct answer is:
[tex]\[ x^2 + (x - 2)^2 = 100 \][/tex]
