If you were told to draw a rectangle along the lines of a sheet of graph paper such that its area is 40 squares, you could choose rectangles measuring 8x5, 10x4, 20x2 or 40x1.

For two of these, 8x5 or 10x4, you would find that you could draw a diagonal across the rectangle that would pass through exactly 12 squares.

What is the smallest number of squares that could be the area of three different rectangles whose diagonals pass through the same number of squares? How many squares does this diagonal pass through?

(In reply to Gentle Reply to Charlie by Jonathan Chang)

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rec·tan·gle <IMG height=18 src="http://perplexus.info/Image1.gif" width=20>(rekÆtangÅgÃl), n.

a parallelogram having four right angles.

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par·al·lel·o·gram <IMG height=18 src="http://perplexus.info/Image2.gif" width=20>(parÅÃ lelÆÃ gramÅ), n.

a quadrilateral having both pairs of opposite sides parallel to each other.

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Nowhere does this rule out having equal sides, that is, being a square. In fact:

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square <IMG height=18 src="http://perplexus.info/Image3.gif" width=20>(skwâr), n.,–n.

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1. a rectangle having all four sides of equal length.

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Posted by Charlie on 2005-04-30 14:37:32