Questions about the world of GRE Math from other sources and general math related questions.
kwame.appau
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Any Idea about this Math question?

by kwame.appau Sat Jul 19, 2014 1:27 pm

"Given enough wood to build a fence with a length of 40 feet, how many ways could you build a rectangular fence that encloses an area of at least 80ft squared? ( using a minimum of 1 foot increment)" Source: GREquestionaday.com
The answer = 5 ways ( 10*10, 9*11, 8*12, 7*13 and 6*14)
please any Idea of how they arrived at this answer. they didn't give any further explanation. Thanks.
tommywallach
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Re: Any Idea about this Math question?

by tommywallach Sun Jul 20, 2014 5:31 pm

Hey Kwame,

Well, the "perfect" shape for a rectangle is a square (if you have to make a rectangle with some perimeter, a perfect square will contain the greatest possible area). The more you "stretch out" a square (making it a thinner and thinner rectangle), the more the area decreases.

So if you have to build a fence with a length of 40 feet, you know the "perfect" shape (in terms of maximizing interior area) is a square, which would be 10x10, with an area of 100.

From there, because we need to use integer values, we can simply check all the other options until the area is no longer 80 ft.

10 x 10 = 100
9 x 11 = 99
8 x 12 = 96
7 x 13 = 91
6 x 14 = 84
5 x 15 = 75 (this one is less than 80, so we know we're done).

Make sense?

-t
kwame.appau
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Re: Any Idea about this Math question?

by kwame.appau Mon Jul 21, 2014 3:17 pm

Yeah. But if we have to build a fence with a length of 40ft, Doesn't it not mean the the length of any of the fence will be constantly 40?
I can't find how the 40ft is handle in your explanation so if you can still please make it clear. Thanks a lot.
tommywallach
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Re: Any Idea about this Math question?

by tommywallach Fri Jul 25, 2014 12:21 pm

Hey Kwame,

A square that is 10 by 10 has a perimeter of 40 (10 + 10 + 10 + 10).

A rectangle that is 9 x 11 has a perimeter of 40 (9 + 11 + 9 + 11).

And so on.

To be clear, in this case "length" is a way to say "perimeter," not just a version of length versus width. If the original question said "length," that is VERY confusing. Is that OUR question? (Gosh, I hope not.)

-t
kwame.appau
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Re: Any Idea about this Math question?

by kwame.appau Fri Jul 25, 2014 4:56 pm

No please. This is not Manhattan prep question. But I now understand the point you have made because I was confused with "length" as it is in the question. But I guess it should be perimeter.
Thanks a lot :)
tommywallach
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Posts: 1917
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Re: Any Idea about this Math question?

by tommywallach Fri Aug 01, 2014 10:25 pm

Glad to help!

-t