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Math (:

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My answer doesn't make sense. It's too big.

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 47 feet?

  • Math (: -

    I have seen this question many times.

    Your answer might be right, try sketching your diagram with the half-circle on the long side of the rectangle, if I recall that is what the shape actually looks like.
    Does your answer make sense now?

  • Math (: -

    No. Sorry :[

  • Math (: -

    let the radius of the circle be x
    then the base of the rectangle on which the circle sits is 2x
    let its height be y
    perimeter = 2x + 2y + 1/2(2pix)
    y = (47-2x-pix)/2

    Area = 2xy + (1/2)pi(x^2)
    = 2x(47-2x-pix)/2 + (1/2)pi(x^2)
    = x(47-2x-pix) + (1/2)pi(x^2)
    = 47x - 2x^2 - pix^2 + (1/2)pi(x^2)

    d(Area)/dx = 47 - 4x - 2pix + pix
    = 0 for a max/min of Area

    solving this I got x = 6.58
    so the base is 13.16
    and after substituting back for y, I got
    y = 6.58 as well

    subbing that back in my Area equation , I got Area = 154.657

    How does that match up with your answers?

  • Math (: -

    My answer was around the thousands. That's how I knew it was wrong. Thanks!

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