In the diagram below, there is a rectangle made of 10 squares, each of a different size. If the dimensions of the two smallest squares in the figure are 3x3 and 5x5, can you determine the dimensions of all the other squares?
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Solution to the Problem:
The dimensions of the squares are 3x3, 5x5, 6x6, 11x11, 17x17, 19x19, 22x22, 23x23, 24x24, and 25x25.To solve, let x = the length of the segment indicated in the diagram below. Then represent the lengths of other segments in the diagram in terms of x.
Since the opposite sides of a rectangle are congruent, you can solve for x by setting the two expressions equal to each other:
(2x - 27) + (x - 16) + 5 + (x - 3) = x + (x + 3)
4x - 41 = 2x + 3
2x = 44
x = 22
Now go back and substitute 22 for x in all the expressions for the sides.
Here is the complete solution.
The dimensions of the rectangle are 65 x 47.
Click here to download Sreeroopa Sankararaman's very colorful solution
Correctly solved by:
| 1. Celton Perry |
Mountain View High School, Mountain View, Wyoming |
| 2. Sreeroopa Sankararaman | Singapore, Singapore |
| 3. Massimiliano Ceci |
Istituto Tecnico Tecnologico (ITT) "Montani", Fermo, Italy |
| 4. Emanuele Greci |
Istituto Tecnico Tecnologico (ITT) "Montani", Fermo, Italy |
| 5. Valerio Giusti |
Istituto Tecnico Tecnologico (ITT) "Montani", Fermo, Italy |
| 6. James Alarie | Flint, Michigan |
| 7. Juan Moncada | San Francisco de Campeche, Mexico |