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An extra square (Posted on 2002-04-30) Difficulty: 3 of 5

Where did the exra square in shape "B" come from?

See The Solution Submitted by levik    
Rating: 4.0769 (13 votes)

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Solution Solution | Comment 7 of 15 |
Green triangle area = 8*3/2 = 12
Sky blue triangle area = 5*2/2 = 5
Orange-yellow area in A = 15
Orange-yellow area in B = 8*2 = 16

The area of the figure A is 12 + 5 + 15 = 32
The area of the figure B is 12 + 5 + 16 = 33
Figure B is bigger than A, so we subtract B - A = 33 - 32 = 1

The extra square in B comes from the diference of the figures A and B, representing an invisible figure in A composed by 2 triangles of sides √29, √73 and √194. The area of these two triangles will give an area of 1, the extra square.
  Posted by Antonio on 2003-08-24 06:04:17
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