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

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Math Expert
Joined: 02 Sep 2009
Posts: 50617
The area of a rectangular playground is 192 square meters. What is the  [#permalink]

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05 Sep 2018, 23:37
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Difficulty:

35% (medium)

Question Stats:

81% (00:33) correct 19% (00:36) wrong based on 16 sessions

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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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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.

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