GAUSS7 2023 Problem 21

Eight-sided polygon A B C D E F G H has integer side lengths. It can be divided into a rectangle and a square, as shown. The area of the square is greater than the area of the rectangle. The product of the two areas is equal to 98. Which of the following could be the perimeter of A B C D E F G H?

Image

Answer Choices
A. 51
B. 32
C. 44
D. 34
E. 33