Question 705267
If you build a gazebo floor in the shape of a regular hexagon, each side measuring 10 feet. The floor requires 2 support beams running vertically, each measures 17.4 feet. If we now plan to build floor larger, using sides of 12 feet, what are the lengths of each support beam?
The "vertical" supports for 10' sides are 10sqrt(3) feet =~ 17.32 ft
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It's a linear relationship, so for 12'
10/sqrt(300) = 12/x
x = 12sqrt(3) =~ 20.78 ft

I got 20.88 feet,
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NOW, If the longest beams that we can purchase are 15 feet, what would be the lengths of each side of the hexagon?
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10/sqrt(300) = x/15
x = 8.66 ft