SOLUTION: Can someone please help me, I've got answer to first part of question, but am struggling with second one. Please double check first if can also. Bless your heart for the help. I

Question 705267: Can someone please help me, I've got answer to first part of question, but am struggling with second one. Please double check first if can also. Bless your heart for the help.
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?
I got 20.88 feet,
NOW, If the longest beams that we can purchase are 15 feet, what would be the lengths of each side of the hexagon?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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
-----------
It's a linear relationship, so for 12'
10/sqrt(300) = 12/x
x = 12sqrt(3) =~ 20.78 ft
I got 20.88 feet,
============================
NOW, If the longest beams that we can purchase are 15 feet, what would be the lengths of each side of the hexagon?
--------------
10/sqrt(300) = x/15
x = 8.66 ft

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