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    What is the area of the largest rectangle that can be drawn inside a circle of diameter 1?

    not sure how i should approach this?
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    I'm guessing equilateral. :awesome:

    Am I helpful yet?

    edit:
    I actually read 'triangle'. My guess still stands, though.
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    draw a circle with Diameter 1, draw a rectangle as big as it can be and measure
    and you could use ratio
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    Draw it.
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    Surely a square...? You can split the square by its corners into 4, to get 4 little isosceles triangles, each with two sides of 0.5.

    You can then work out the area of one traingle and multiply by 4.
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    Divide the circle into four equal sections.
    You can then work out the length of one side of the square, using the cosine rule:
    a^2 = b^2 + c^2 -2bcCosA
    x^2 = 0.5^2 + 0.5^2 -2\times1\times1Cos\frac{\pi}{2}
    Where x is the length of the side
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    First notice that the diagonal of the rectangle is the diameter of the circle.

    Let l be the length of one of the sides then you can use Pythagoras' theorem to find the length of the adjacent side in terms of l. Now you should have a formula for the area of the rectangle in terms of l.

    You need to use differentiation to find the maximum area. Have a go and post again if you're stuck.
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    (Original post by maxfire)
    Divide the circle into four equal sections.
    You can then work out the length of one side of the square, using the cosine rule:
    a^2 = b^2 + c^2 -2bcCosA
    x^2 = 0.5^2 + 0.5^2 -2\times1\times1Cos\frac{\pi}{2}
    Where x is the length of the side
    Maybe easier to use  Area= {1}/{2}absinC

    where a and b = 0.5 and sinC=pi/2

    Then multiply by 4.
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    what notnek said is the procedure you should use.
 
 
 
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