A window of fixed perimeter (including the base of the arc) is in t...

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A window of fixed perimeter (including the base of the arc) is in the form of a rectangle surrounded by a semi-circle. The semi-circular portion is filled with coloured glass while the rectangular part is filled with clear glass. The clear glass transmits three times as much light per square metre as the coloured glass does. What is the ratio of the sides of the rectangle so that the window transmits the maximum light ?
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