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The area of a rectangular playground is 192 square meters. What is the

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The area of a rectangular playground is 192 square meters. What is the  [#permalink]

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New post 05 Sep 2018, 23:37
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The area of a rectangular playground is 192 square meters. What is the perimeter of the playground?

(1) The length of the playground is three times the width of the playground .
(2) If the width of the playground were doubled, then the ratio of the length to the width would be 3 : 2

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Re: The area of a rectangular playground is 192 square meters. What is the  [#permalink]

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New post 06 Sep 2018, 02:31
[quote=]The area of a rectangular playground is 192 square meters. What is the perimeter of the playground?

(1) The length of the playground is three times the width of the playground .
(2) If the width of the playground were doubled, then the ratio of the length to the width would be 3 : 2[/quote]

let the length be L and the Width W
We know \(L*W=192\).......................(i)
\(Perimeter=2(L+W)\)........................(ii)

Statement 1: The length of the playground is three times the width of the playground
This implies, \(L=3W\).......................(iii)
We can substitute L in (i) and solve the quadratic to calculate \(W\)
and using (ii), we can get L and hence calculate the Perimeter using (iii)
Sufficient.

Statement 1: If the width of the playground were doubled, then the ratio of the length to the width would be 3 : 2
This implies, \(W'(New Width)=2W\)
Therefore, \(\frac{L}{2W} = \frac{3}{2}\)
We can substitute either of L or W from this equation into (i) to solve the quadratic and again use the above equation to calculate the other variable.
Using (ii), we can calculate the Perimeter.
Sufficient.

Answer: D
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Re: The area of a rectangular playground is 192 square meters. What is the   [#permalink] 06 Sep 2018, 02:31
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