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iSquared Magazine

The Daily Rant

Puzzles
Dividing a square

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Here's a geometry puzzle to keep you occupied. The square pictured at left has been divided into three pieces by making two parallel cuts. The three resulting pieces have equal areas. The middle piece (the almost-diagonal strip) is 10 inches wide. What is the area of the whole square?

Good luck!

Courtesy of Mark Nielsen

 
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lydiaeniola260704:12:40, 10 May 08
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12inches i think

 
terveloc14:13:30, 17 Nov 07
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1300 looks right to me.

 
henklaak16:07:20, 12 Oct 07
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SPOILER AHEAD, TRY TO DO IT YOURSELF FIRST !!

Assume the green triangle has height h and width w.

All areas are size: 1/3 h^2
Green area = w h / 2
Follows: w = 2/3 h

The yellow area is also 10 x the diagonal:
1/3 h^2 = 10 sqrt (h^2 + 4/9 h^2)
1/3 h = 10 sqrt(13/9)
Follows: h = 10 sqrt(13)

Total area = h^2 = 100 * 13 = 1300

 


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