A window frame is shaped like a rectangle with an arch forming the top ( ie; a box with a semicircle on the top)

The vertical straight side is Y, the width at the base and at the widest part of the arch (Diam) is X.

I know that the perimeter is 4.

Find X if the area of the frame is at a maximum?

Joshi sir comment

perimeter = 4 so 2Y + X + πX/2 = 4

and area = XY + [π(X/2)2]/2

put Y from 1st equation to 2nd we get A = X[4-X{1+(π/2)}]/2 + πX2/8

now calculate dA/dX and then compare it to zero

X will be 8/(4+π)

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PRATEEK PANDEY 9 year ago is this solution helpfull: 0 0

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