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Note: This is from the Po Leung Kuk 2012 paper. The previous one I posted was from the Po Leung Kuk 2011.
Here's another question for everyone:
There is a figure made out of two rows of identical squares: three squares in the top row and four in the bottom, so that the first three squares in the bottom row form a $2\times 3$ rectangular block of squares with the squares of the first row. (If anyone knows how to insert a diagram, please do so.) A line, $l$, passes through the top side of the second square on the top row at point $E$ and passes through the bottom side of the third square from the bottom row at point $F$. Line $l$ cuts the figure into 2 equal pieces.
Let the top left corner of the figure be point $A$ and the bottom left be point $C$. If $AE+CF=91$, what is the area of an individual square.
I have no idea on how to approach this problem. A hint on how to start the problem is good enough. Also, if anyone knows how to create a diagram, please put it in the comments.
Thanks!

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  • $\begingroup$ Is the figure perfectly symmetric about the line between the 2nd and 3rd squares on the bottom row? $\endgroup$ – JimmyK4542 Jun 11 '14 at 2:44
  • $\begingroup$ nope. Both rows start from the same column. $\endgroup$ – user148697 Jun 11 '14 at 2:46
  • $\begingroup$ @jonnytan999 I guess the hardest part of this question is -- (1) guessing what the figure looks like from your description; and (2) The meaning of your 'EQUAL' [are the two equal pieces EQUAL in AREA or EQUAL in shape! $\endgroup$ – Mick Jun 11 '14 at 15:18
  • $\begingroup$ can you tell me how to insert the diagram, please... $\endgroup$ – user148697 Jun 12 '14 at 5:03
  • $\begingroup$ @jonnytan999 When your accumulated credit has reached a critical value (say, 100, I guess), you will then be entitled to include diagrams in your question. By that time, your tool bar will then be changed to “Bold, Italic, Link, Quote, Bracket, (Picture link)…”. Through that (Picture link), your post can then be incorporated with pictures uploaded directly from your computer. At present, you can still upload your picture to some (free) picture hosting websites first. They will give you a link to the picture hosted. Then, include that link via your “link” button in your post. Good luck. $\endgroup$ – Mick Jun 12 '14 at 14:37
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Let $x$ be the sidelength of a square. Then the area of the entire figure is $7x^2$.

One half of the figure is quadrilateral $ACFE$, which is a trapezoid with height $2x$ and bases $AE$ and $CF$.

Can you figure out the area of this trapezoid in terms of $x$? Then, you should be able to figure out what value of $x$ makes this trapezoid have an area of half the area of the figure.

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  • $\begingroup$ Oh Yeah! Why didn't I think of that? Bangs head on wall. +1 $\endgroup$ – user148697 Jun 11 '14 at 2:53

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