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# The area of square S is equal to the area of rectangle R. What is the

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Math Expert
Joined: 02 Sep 2009
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The area of square S is equal to the area of rectangle R. What is the [#permalink]

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19 Nov 2017, 09:48
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71% (01:02) correct 29% (01:04) wrong based on 41 sessions

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The area of square S is equal to the area of rectangle R. What is the perimeter of square S?

(1) The length of one of the sides of rectangle R is twice the length of a side of square S.

(2) The area of rectangle R is 36.
[Reveal] Spoiler: OA

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The area of square S is equal to the area of rectangle R. What is the [#permalink]

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19 Nov 2017, 09:52
Bunuel wrote:
The area of square S is equal to the area of rectangle R. What is the perimeter of square S?

(1) The length of one of the sides of rectangle R is twice the length of a side of square S.

(2) The area of rectangle R is 36.

Given $$a^2=l*b$$ where $$a$$ is the length of the square and $$l$$ & $$b$$ is the length and breadth of the rectangle

we need to find Perimeter $$= 4a$$. Hence we need values of $$l$$ & $$b$$

Statement 1: implies $$l=2a$$. but nothing mentioned about breadth of the rectangle. Hence insufficient

Statement 2: $$l*b=36=a^2$$

so $$a=6$$. Hence $$4a=4*6=24$$. Sufficient

Option B
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Re: The area of square S is equal to the area of rectangle R. What is the [#permalink]

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19 Nov 2017, 12:28
Info: Area of square S = Area of rectangle R
Ques: Perimeter of square S = ?

If a be the side of square S, and l & b be the length & breadth respectively of rectangle R, then what do we know and what do we want:-
we know that $$a^2$$=l*b, and
we want the value of a

St (1) The length of one of the sides of rectangle R is twice the length of a side of square S.
This implies that either length l or breadth b = 2a, but as different values can be taken for both l & b, statement 1 is insufficient.

St (2) The area of rectangle R is 36.
So, l*b=36, and from ques info we know that area of rectangle = area of square, which implies that, $$a^2$$=36, or, a=6, from which we can find the perimeter of square S.
Therefore, statement (2) is sufficient, hence, answer choice B.
Re: The area of square S is equal to the area of rectangle R. What is the   [#permalink] 19 Nov 2017, 12:28
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