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

Question

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.

pankajvashist · Answer

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.

GMATinsight · Answer

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!

mvictor · Answer

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.

BillNella89 · Answer

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.

Answer: C

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

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