What is the relationship between the arches of the regular hexagons constructed on the sides of the right triangle below?

Answer: the sides correspond to lengths 3, 4, and 5
Explanation: We are given the areas A of the regular hexagons. The general formula for an area of such a hexagon is:
[tex]A=\frac{3\sqrt{3}}{2}a^2[/tex]
where a is the side length of the hexagon.
Use the formula to solve for a:
[tex]a = \sqrt{\frac{2A}{3\sqrt{3}}}[/tex]
for the three hexagon areas we are given:
a = 5 (yellow)
a = 4 (blue)
a = 3 (red)
Please let me know whether this answers your question, or whether you were looking for another type of relationship statement