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What is the perimeter of rectangle R ?

This topic has 2 expert replies and 1 member reply
sachin_yadav Master | Next Rank: 500 Posts
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What is the perimeter of rectangle R ?

Post Thu Jul 24, 2014 5:50 am
What is the perimeter of rectangle R ?
(1) R is a square.
(2) The area of R is 36.

OA is C

Please explain

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GMATinsight Legendary Member
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Post Fri Jul 25, 2014 2:26 am
sachin_yadav wrote:
What is the perimeter of rectangle R ?
(1) R is a square.
(2) The area of R is 36.

Please explain
Question : What is the perimeter of rectangle R?

Let, L be the Length and W be the Width of the rectangle then

Question Rephrased : 2(L+W) = ?

Statement 1) R is a square
i.e L = w therefore perimeter = 2(L+W) = 2(L+L) = 4L
But L is unknown therefore INSUFFICIENT

Statement 2) The area of R is 36
i.e. LxW = 36
Case 1: L = 6 and W = 6 then Perimeter = 2(L+W) = 24
Case 2: L = 9 and W = 4 then Perimeter = 2(L+W) = 26
INCONSISTENT Answer Therefore INSUFFICIENT

Combining the Two statements
L = W and LxW = 36
i.e. L^2 = 36 i.e. L = W = 6
Therefore, Perimeter = 2(L+W) = 2(6+6) = 24

SUFFICIENT

Answer: Option C

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Post Thu Jul 24, 2014 9:14 pm
Hi sachin_yadav,

You'll notice that Brent's approach focused heavily on considering the multiple possibilities that could fit each piece of information (the 2 Facts underneath the prompt). This approach is a rather important part of getting DS questions correct, so you should be thinking about whether a given Fact leads to just one possible answer or if it leads to more than one possible answer. Get in the habit of taking notes, drawing pictures and proving what's possible. You'll see your score improves significantly as a result.

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Rich

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GMAT/MBA Expert

Post Thu Jul 24, 2014 6:12 am
sachin_yadav wrote:
What is the perimeter of rectangle R?

(1) R is a square.
(2) The area of R is 36.
Target question: What is the perimeter of rectangle R?

Statement 1: R is a square
Since R can be a square of ANY SIZE, then it can have ANY perimeter.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: A square is a TYPE of rectangle

Statement 2: The area of R is 36
There are MANY rectangles that satisfy this condition. Here are two:
Case a: rectangle R could have height 6 and width 6 (so the area is 36), in which case the perimeter is 24
Case b: rectangle R could have height 3 and width 12 (so the area is 36), in which case the perimeter is 30
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that R is a square
Statement 2 tells us that this SQUARE has area 36
There's ONLY ONE square in the universe that has area 36, and that's a square in which all sides have length 6. If all sides have length 6, then the perimeter of R is 24
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

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