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# The figure shown below has area A. If the length of each

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The figure shown below has area A. If the length of each [#permalink]

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12 Aug 2004, 20:16
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The figure shown below has area A. If the length of each side were doubled, what would then be the area in terms of A ?

A. 2A
B. 4A
C. 6A
D. 8A
E. 10A

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ps.JPG [ 5.46 KiB | Viewed 863 times ]

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12 Aug 2004, 20:59
B. 4A.

We know, XL + (Y-X)(L-M) = A

New Area is 2X*2L + (2Y-2X)(2L-2M)
=>4XL + 4 (Y-X)(L-M)
=>4A.

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12 Aug 2004, 21:47
I sketch a little graph and got B)4A in 45 sec.
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Paul

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13 Aug 2004, 07:13

Paul, how did you solve using the graph ? I am trying to find out easy way to do problems for which I took a long time.
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13 Aug 2004, 07:57
The portion in red is original the figure. The yellow portion is when every side is multiplied by 2. You can clearly see the 4A if red portion is A.
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Paul

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13 Aug 2004, 08:13
40s. 4A
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CIO
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13 Aug 2004, 11:47
I saw this as a plug in, pure and simple (and I don't like plugging in too often - only where it makes perfect sense - here it did).

Since there's clearly an answer, and we're doubling every amount, and it's all proportional, then I just put down possible values for every side, got the area, and did it again with those values doubled.

Paul, I dug your method, too.
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13 Aug 2004, 13:30
If you think about the shape as a rectangle (with a missing segment), then doubling each side results in a rectangle 4 times the size (with a missing segment of 4 times the size as well)... Hence 4A.
13 Aug 2004, 13:30
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