Can you find other rectangles with the same area?
Factors, Prime Numbers, Diophantine Equations, Graphs of Reciprocal Functions
Can you find rectangles with the same perimeter but minimum/maximum area?
Calculus, proof 
Can you find other rectangles with area = perimeter?
Graph transformations, algebraic proof, asymptotes

Click on the image to enlarge.

What questions could you ask about this picture?

For example: 'How many other rectangles have area = 80 sq cm?'