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# If l and w represent the length and width, respectively, of the rectan

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SVP
Joined: 08 Jul 2010
Posts: 2017
Location: India
GMAT: INSIGHT
WE: Education (Education)
If l and w represent the length and width, respectively, of the rectan [#permalink]

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09 Sep 2015, 11:35
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Question Stats:

76% (00:59) correct 24% (01:06) wrong based on 106 sessions

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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.
[Reveal] Spoiler: OA

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Joined: 10 Jan 2013
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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
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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.

Can somebody explain the problem.
SVP
Joined: 08 Jul 2010
Posts: 2017
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If l and w represent the length and width, respectively, of the rectan [#permalink]

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09 Sep 2015, 23:28
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Expert's post
GMATinsight wrote:
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

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.
Intern
Status: Prepping for GMAT
Joined: 06 Nov 2017
Posts: 19
Location: France
GPA: 4
Re: If l and w represent the length and width, respectively, of the rectan [#permalink]

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01 Mar 2018, 05:31
GMATinsight wrote:
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.

Rephrasing the question: "what is the perimeter of the rectangle?" i.e. $$2*(l+w) = ?$$

(1) The area of the rectangle is 48
Mathematically, this means that $$l*w = 48$$. This piece of information is not sufficient by itself.
Hence, the statement is insufficient (eliminate A and D).

(2) The length of a diagonal of the rectangle is 10
Since, rectangles have right angles in their corners, the diagonal of any rectangle can be obtained through Pythagoras' theorem. Mathematically, this means that $$\sqrt{l^2+w^2} = 10$$. This piece of information is not sufficient by itself.
Hence, the statement is insufficient (eliminate B).

(1) + (2) The area of the rectangle is 48 and the length of a diagonal of the rectangle is 10
This statement gives us two mathematical formulas:
$$l*w = 48$$
$$\sqrt{l^2+w^2} = 10$$
If one recalls, one of the basic mathematical identities is $$(a+b)^2 = a^2 + 2*ab + b^2$$. Hence, if we plug the two formulas above into the latter identity, we get:
$$(l+w)^2 = l^2 + w^2 + 2*l*w = 10^2 + 2*48 = 196 = 14^2$$
Thus, $$2*(l+w) = 2*14 = 28$$.
This is sufficient to answer the question.

Re: If l and w represent the length and width, respectively, of the rectan   [#permalink] 01 Mar 2018, 05:31
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