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# The average length of all the sides of a rectangle equals twice the

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Joined: 12 Aug 2015
Posts: 2638
Schools: Boston U '20 (M)
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The average length of all the sides of a rectangle equals twice the  [#permalink]

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11 Apr 2017, 09:46
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Difficulty:

35% (medium)

Question Stats:

71% (02:18) correct 29% (02:42) wrong based on 60 sessions

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The average length of all the sides of a rectangle equals twice the width of the rectangle.If the area of the rectangle is 18,what is its perimeter?

A)6√6
B)8√6
C)24
D)32
E)48

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Re: The average length of all the sides of a rectangle equals twice the  [#permalink]

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11 Apr 2017, 10:18
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stonecold wrote:
The average length of all the sides of a rectangle equals twice the width of the rectangle.If the area of the rectangle is 18,what is its perimeter?

A)6√6
B)8√6
C)24
D)32
E)48

l*b = 18 -------- given

(2b+2l)/4 = 2b
6b = 2l
3b = l
3*18/l = l (using the given data)
$$l^2$$ = 54
l = 3√6
therefore b = √6

perimeter = 2*(3√6+√6) = 8√6

Hence option B is correct
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Joined: 22 May 2016
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The average length of all the sides of a rectangle equals twice the  [#permalink]

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30 Apr 2017, 11:40
0akshay0 wrote:
stonecold wrote:
The average length of all the sides of a rectangle equals twice the width of the rectangle.If the area of the rectangle is 18,what is its perimeter?

A)6√6
B)8√6
C)24
D)32
E)48

l*b = 18 -------- given

(2b+2l)/4 = 2b
6b = 2l
3b = l
3*18/l = l (using the given data)
$$l^2$$ = 54
l = 3√6
therefore b = √6

perimeter = 2*(3√6+√6) = 8√6

Hence option B is correct
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0akshay0 I have what might be a dumb question whose answer might be glaringly obvious, sorry! The prompt refers to the "average length of all sides."

When solving for area in this problem in order to get a side length, see highlight, how do we know that length equals side such that in the equation we can simply divide by L as you did?

I was tempted to do the same, but I was unsure about this issue. I solved the same way you did up to L=3W (your "b"). Then instead:

L*W = 18
3W*W = 18
W$$^2$$ = 6
W= √6

Perimeter = 2W + 2L
= 2W + 2(3W)
= 2√6 + 6√6 = 8√6

I think the answer has something to do with weighted averages, but I have fog brain
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The average length of all the sides of a rectangle equals twice the &nbs [#permalink] 30 Apr 2017, 11:40
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