Can someone explain how to do this data sufficiency problem?

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vladig172: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Aug 20, 2009 5:01 am

by vladig172 » Thu Aug 20, 2009 5:12 am

Hi guys,

I'm stuck on a DS problem in OG 12 Diagnostic Test Q48:

If p is the perimeter of rectangle Q, what is the value of p?

(1) Each diagonal of rectangle Q has length 10
(2) The area of rectangle Q is 48

I got this questions wrong, and the correct answer is...C. I went through the explanation, and feel it is unreasonably complicated ... there's now way most could do all that in 2 minutes or less... I answered E on the basis of there being a quadratic involved, and thus producing two answers. Yet in this case, the problem can be solved. Is there some rule I'm missing? Thoughts?

Thanks for the help
-vlad

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Source: Beat The GMAT — Data Sufficiency | Thu Aug 20, 2009 5:12 am

acenikk: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Fri Jul 31, 2009 6:41 am; Thanked: 1 times

by acenikk » Thu Aug 20, 2009 6:10 am

Let one side of the rectangle be a, and another side be b. Perimeter will be 2*(a+b).

From 1, a^2 + b^2 = 100
From 2, ab = 48

(a+b)^2 = a^2 + b^2 + 2ab
= 100 + (2*48)
= 196
So (a+b) = sqrt(196) = 14.

Hence, Perimeter is 2*(a+b) = 2 * 14 = 28.

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vladig172: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Aug 20, 2009 5:01 am

Brilliant.

by vladig172 » Thu Aug 20, 2009 9:11 am

That's an impressive answer. Thank you.

Is this a trick that you simply know to look for? Or did you figure it out through trial and error?

I'm trying to learn the right way to think through these types of problems.

Thank you again,
-vlad

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GID09: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Sat Jan 17, 2009 3:48 pm; Thanked: 1 times

by GID09 » Thu Aug 20, 2009 9:59 am

Just curious, Can we assume rectangle to be two 30-60-90 degree traingles?

In which case diagonal length is enough to answer the question. Please advise.

GID09

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vladig172: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Aug 20, 2009 5:01 am

not sure about that

by vladig172 » Thu Aug 20, 2009 10:30 am

I don't believe that's a standard rule (is it?). My understanding is the angles would depend upon the width/height of the rectangle, since it's not a square (in which you could assume 45/45/90)

-v

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