How I can find the largest area of a rectangle with a half-cycle on it and a given perimeter?

This image can help someone http://img132.imageshack.us/img132/3809/semirectanglexf6.png is trying to make the form of tape, and there are a total of 20 m of tape. The person who is trying to maximize the area of a rectangle, which would the dimensions of the larger rectangle area?

L is the side that is a semicircle. B is the other side of the rectangle. = Length of perimeter upper semicircle = sum of three sides of the rectangle lx .= 25 pi / 2 + l + 2b = 25 l (1 + pi / 2) 2 b = 25 ….( 1) to (1): b = 12, 5 – l (1 + pi / 2) / 2 …….( 2) Area of a rectangle pound = Substituting the value of b of (2) a = lx (12.5 – l (1 + pi / 2) / 2) Simplify: a = 12.5L – ^ l 2 (12.5 – L (1 + pi / 2) / 2) gives a maximum / dl = 0 da / dl = 12.5 – l (1 + pi / 2) = 0 = 12.5 l / (1 + pi / 2) b = 12.5 to 12.5 / (1 + pi / 2) 2 = 12.5 / 2 = 6.25 These are the required values. A review shows that the perimeter is 25

Area of a Rectangle – YourTeacher.com – Geometry Help

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