1. **Stating the problem:** We have a rectangle with length $x$ and width $y$. We need to determine which statements about its perimeter and area are true. 2. **Formulas:** - The perimeter $P$ of a rectangle is given by $$P = 2(x + y)$$ because the perimeter is the sum of all sides: two lengths and two widths. - The area $A$ of a rectangle is given by $$A = xy$$ because area is length times width. 3. **Evaluating each statement:** - A. The perimeter is $x + y$. This is incorrect because perimeter includes both lengths and widths twice. - B. The perimeter is $xy$. This is incorrect; $xy$ is area, not perimeter. - C. The perimeter is $2(x + y)$. This is correct by the perimeter formula. - D. The perimeter is $2xy$. This is incorrect; $2xy$ is not the perimeter. - E. The perimeter is $2x + 2y$. This is correct and equivalent to $2(x + y)$. - F. The area is $x + y$. This is incorrect; area is product, not sum. - G. The area is $xy$. This is correct by the area formula. - H. The area is $2xy$. This is incorrect; area is $xy$, not doubled. 4. **Summary:** The true statements are C, E, and G.