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# area watch

1. 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?
2. I'm guessing equilateral.

edit:
I actually read 'triangle'. My guess still stands, though.
3. draw a circle with Diameter 1, draw a rectangle as big as it can be and measure
and you could use ratio
4. Draw it.
5. 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.
6. Divide the circle into four equal sections.
You can then work out the length of one side of the square, using the cosine rule:

Where x is the length of the side
7. 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.
8. (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:

Where x is the length of the side
Maybe easier to use

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

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

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