1. The problem involves a rectangle with a diagonal of length 10 units. 2. We want to find the dimensions of the rectangle or verify the relationship between its sides and the diagonal. 3. Recall the Pythagorean theorem for a rectangle: if the sides are $a$ and $b$, and the diagonal is $d$, then $$d^2 = a^2 + b^2$$ 4. Given $d = 10$, we have $$10^2 = a^2 + b^2$$ which simplifies to $$100 = a^2 + b^2$$ 5. Without additional information about $a$ or $b$, this is the fundamental relationship between the sides and the diagonal. 6. If the sides are given or can be inferred, substitute and solve for the unknown side. 7. For example, if one side is 6, then $$100 = 6^2 + b^2 = 36 + b^2$$ 8. Subtract 36 from both sides: $$100 - 36 = b^2$$ 9. Using cancellation notation: $$\cancel{100} - \cancel{36} = b^2$$ (just showing the subtraction step) 10. Simplify: $$64 = b^2$$ 11. Taking the square root of both sides: $$b = \sqrt{64} = 8$$ 12. So, if one side is 6, the other side is 8, and the diagonal is 10, confirming the Pythagorean triple (6, 8, 10). Final answer: The sides satisfy $$a^2 + b^2 = 100$$ and if one side is 6, the other is 8.