Problem of the Day #54

POTD January 28, 2024

Let ABCD be a unit square. Let EFGH be a rectangle inside of ABCD such that E,F,G are on BC,CD,DA, respectively, and A,E,H collinear. If the longer side of the rectangle is \frac{7}{3} of the shorter side of the rectangle, and the area of the rectangle can be expressed as \frac{a}{b}, where a and b are positive, coprime integers, find a+b.