Question 553984: This is a personal question, just wondering how i could solve it, however i will accept an answer.
If a beehive makes crops take less time to get to a harvesting stage, and a beehive covers a Circle with a radius of 13 Meters. How large of a square could i put inside of the Circle so that the most crop area was covered? I thought it would be 18 Meters x 18 meters, but it doesn't seem to work. Any Ideas?
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! If a beehive makes crops take less time to get to a harvesting stage, and a beehive covers a Circle with a radius of 13 Meters. How large of a square could i put inside of the Circle so that the most crop area was covered? I thought it would be 18 Meters x 18 meters, but it doesn't seem to work. Any Ideas?
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The diagonal of the square is the diameter of the circle, = 26 meters.
The sides of the square = 
s =~ 18.385 meters
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! circle has a radius of 13 meters which means that the diagonal of a square that is inscribed in the circle will be 26 meters.
this means that a side of the square will be equal to 18.38477631
this means that the crop area to be covered will be 18.38477631^2 = 338 square meters.
the area of the circle itself will be equal to pi*r^2 = pi*13^2 = 530.9291585 square meters.
a picture of what i believe you are asking about is shown below:
the sides of the square and the diagonal of the square form a right triangle.
in a right triangle, the hypotenuse is equal to the sum of the squares of each leg.
if you let s = the length of each leg, then you get:
s^2 + s^2 = 26^2 which gets you:
2s^2 = 676
divide both sides of this equation by 2 gets you:
s^2 = 338
take the square root of both sides of this equation to get:
s = 18.38477631
you were close but no cigars for you this time unless i misunderstood the problem.
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