17. The square $A B C D$ consists of four congruent rectangles arranged around a central square. The perimeter of each of the rectangles is $40 \mathrm{~cm}$. What is the area of the square $A B C D$ ?
A $400 \mathrm{~cm}^{2}$ B $200 \mathrm{~cm}^{2} \mathrm{C} 160 \mathrm{~cm}^{2} \mathrm{D} 120 \mathrm{~cm}^{2} \mathrm{E} 80 \mathrm{~cm}^{2}$
17. A Let the length of each of the rectangles be $x \mathrm{~cm}$ and the width be $y \mathrm{~cm}$. The perimeter of each of the rectangles is $40 \mathrm{~cm}$ and hence $2 x+2 y=40$. Therefore $x+y=20$. From the diagram we can see that the length of each side of the square $A B C D$ is $(x+y) \mathrm{cm}$. Therefore the square $A B C D$ has side length $20 \mathrm{~cm}$. Hence the area of $A B C D$ is $(20 \times 20) \mathrm{cm}^{2}=400 \mathrm{~cm}^{2}$.