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What the problem says:

When a screen is placed $3 m$ from a projector, the picture occupies $3 m^2$. How large will the picture be when the projector is $5 m$ from the screen?

My direct answer would be $5 m^2$, but it seems too easy to be true. I am curious about what the answer would be, or how to do it - it is not something critical since I am doing this in my free time.

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    Note that if you put it twice as far away, 6m, the image is not twice as big, $6m^2$, but four times, $12m^2$, because it is twice as wide and twice as tall.2012-03-19

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