Data Sufficiency

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

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.

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

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

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