beatsinmusic1 beatsinmusic1
  • 07-11-2018
  • Mathematics
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What is the relationship between the arches of the regular hexagons constructed on the sides of the right triangle below?

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

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remotecontrolbrain
remotecontrolbrain remotecontrolbrain
  • 07-11-2018

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

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