A group of students is given a 10 by 10 grid to cut into individual unit squares. The challenge is to create two squares using all of the unit squares. Their teacher states that after the two new squares are formed, one should have a side length two units greater than the other.

Let the larger square have side length x units, so the smaller square has side length x − 2. Their areas are x² and (x − 2)², and together they use all 100 unit squares in the 10 by 10 grid. Thus the equation is x² + (x − 2)² = 100, which is choice C.

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