Thursday, November 13, 2008

Rectangle of Squares 1

Boosted from JD2718
Clarence the Clever Contractor cleared a rectangular plot of land and covered it with gravel. Then he purchased 9 square wooden sections of side-length 2, 5, 7, 9, 16, 25, 28, 33, and 36. By placing the squares on the gravel with no two overlapping, Clarence built a patio which exactly covered the graveled surface. Find the perimeter of Clarence’s new patio.
I have another from an Informal Geometry book, which drew out the squares, labeled the 7 and 9 and left finding the rest of the sides for the students.

If you get the first, try this one ...
7, 9, 16, 19, 26, 28, 33, 44, 45, 60

Try using total area and prime factorization as well as the visual method, which I likened to a sunflower in that you start in the middle and work outwards.

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