SOLUTION: a window has the form of a rectangle surrounded by a semi circle if perimeter is 40 units.find its dimensions so that the area of window is maximum

Question 1041677: a window has the form of a rectangle surrounded by a semi circle if perimeter is 40 units.find its dimensions so that the area of window is maximum
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Assume the window is X wide and Y long.
So then the perimeter of the window would be.

1.
and the area of the window would be,

2.
From eq. 1,

Let's just call the constant in front of X, B, just for better readability.

So then substituting into 2,

Once again, let's use a constant, C.

Convert to vertex form to find the vertex and maximum area.

So the maximum area of

occurs when,

and

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