1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Strain on Brain

  1. Jan 25, 2004 #1
    Ram has a rectangular piece of card board out of which he clipped away the largest possible square and was left with a piece similar in shape to the original piece. The area of the piece remaining with Ram forms approx what percent of the original piece
  2. jcsd
  3. Jan 25, 2004 #2


    User Avatar
    Science Advisor

    This is a "golden rectangle" problem isn't it?

    Let the original rectangle have length l and width w. We an assume that w< l. The largest square that can be cut from that is "w by w" leaving a rectangle of sides w and l-w.

    Now which is larger, w or l-w? If we started with a skinny rectangle, in which l was not only larger than w but larger than 2w, l-w is still larger than w and saying that this new rectangle is similar to the orginal says that l/w= (l-w)/w (writing longer side over shorter for both rectangles). But that's the same as l= l-w which is impossible.

    Thus, in the new rectangle, the longer side (corresponding to l in the original rectangle) has length w and the shorter l-w. Since the new rectangle is similar to the original, we have w/(l-w)= l/w or
    w2= l2- lw. Dividing both sides by l2, (w/l)2= 1- w/l. We can think of this a quadratic equation and solve for w/l.

    The area of the new rectangle is w(l-w)= lw- w2. The area of the original rectangle was lw. The new rectangle has area
    (lw- w2)/lw= 1- (w/l).
  4. Jan 26, 2004 #3
    Thanks Halls I knew i have to apply the prop u quoted but never applied it was just an odd time
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook