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Re: If l and w represent the length and width, respectively, of the rectan [#permalink]

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09 Sep 2015, 23:04

we have to find out the perimeter of the rectangle which is 2( l+w) :

1. The area of the rectangle is 48 --> not sufficient as possible (l,w) can be (4,12),(8,6),( 2,24),(16,3). 2. The length of a diagonal of the rectangle is 10.--> sufficient. As rectangle is right angled and only (8,6) satisfy the equation 10^2= 8^2+6^2.

If l and w represent the length and width, respectively, of the rectangle, what is the perimeter of Rectangle?

(1) The area of the rectangle is 48. (2) The length of a diagonal of the rectangle is 10.

Perimeter = l + w

Statement 1: The area of the rectangle is 48 i.e. l*w = 48 Case 1: l = 6 and w = 8 Case 2: l = 1 and w = 48, Hence, NOT SUFFICIENT

Statement 2: l^2 + w^2 = 10^2 = 100 Case 1: l = 6 and w = 8 Case 2: l = \(5\sqrt{2}\) and w = \(5\sqrt{2}\), Hence, NOT SUFFICIENT

Combining the two statements l and w can only be 6 and 8 (or vice versa) but in each case Perimeter = 2(6+8) = 28 SUFFICIENT

Answer: option C

I hope this helps!
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If l and w represent the length and width, respectively, of the rectan [#permalink]

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27 Oct 2015, 18:55

i spent more time on thinking whether B is a trap or not, since 10 is 2x5, and we know the pythagorean triplet 3-4-5 multiplied by 2 or 6-8-10. even the first statement might suggest that l=8 and w=6 since 6*8 = 48 but!!! if you do the math, you see that lw = 48, and l^2 + w^2 = 100 knowing that (a+b)^2 = a^2+2ab+b^2, we can easily see that l^2+2lw+w^2 = 196 or (l+w)^2 = 196 l+w will thus be 14 and the perimeter 32. we can get to the correct answer only by combining the two statements. C is the answer.

gmatclubot

If l and w represent the length and width, respectively, of the rectan
[#permalink]
27 Oct 2015, 18:55

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