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Packing a Square With Rectangles

This problem was asked by Michalia on Yahoo! Answers...


Imagine that there are five rectangles where the measure of the length and width of each rectangle is a whole number from 1 to 10, and that you can only use each number once. Now imagine that these five rectangles can be fit together to form a square, with no spaces between the rectangles. Draw a sketch of this square showing how each rectangle fits.

Your Task: Solve Michalia's problem, interesting in itself...

THEN, try to understand these solutions...suggested on-line by readers when Michalia's problem was first posted:

  • Jacob writes: "yes its possible because a square can also be a rectangle so just put 5 rectangles sideways or upwards."
  • Ewanwer writes: "a rectangle could be 1 wide by 5 long"
  • Jigglezp writes: "Easy. Four squares and one square four times the size of the other four, put on top of them."
Think about the last one, as it is quite clever (but fails to meet the problem's conditions)!

 


Hint: Start drawing pictures...dividing a square up....

 


Solution Commentary: This was the successful solution offered by Puzzling...

Square = 11 x 11
Rectangle A = 8 x 2
Rectangle B = 3 x 6
Rectangle C = 1 x 9
Rectangle D = 6 x 4
Rectangle E = 10 x 5

Visual proportions are off in picture. a a a a a a a a b b b
a a a a a a a a b b b
c d d d d d d d b b b
c d d d d d d d b b b
c d d d d d d d b b b
c d d d d d d d b b b
c e e e e e e e e e e
c e e e e e e e e e e
c e e e e e e e e e e
c e e e e e e e e e e
c e e e e e e e e e e