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A window of perimeter P (including the b...

A window of perimeter `P` (including the base of the arch) is in the form of a rectangle surrounded by a semi-circle. The semi-circular portion is fitted with the colored glass while the rectangular part is fitted with the clear glass that transmits three times as much light per square meter as the colored glass does. What is the ratio for the sides of the rectangle so that the window transmits the maximum light?

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The correct Answer is:
`(6)/(pi+6) or (pi+6)/(6)`
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