Construct a window in the shape of a semi-circle over a rectangle.If the distance around the outside of the window is 12 feet.What dimensions will result in the rectangle having the largest possible area?

Question

We need to find Amax
I know the circmfrence is 12
12=w+2L+a/2(pie)

I'm not sure about the equation above.

Thank you!

Answer 1

in the equation above, I hope a=w/2
so the length around the top semicircle is PI*a=PI*w/2

12= w+2L+PI w/2
12=w(1+PI/2)+2L
area= wL+1/2 PI (w/2)^2
so solve for L in the perimeter equation, and then put that in for L in the area equation.
Take the derivative of area wrespect to w, set to zero, and solve for w.
Then go back and solve for L.

Answer 2

thanks!!