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Square patio with walkway

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shanewyatt
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Square patio with walkway [#permalink] New post   22 Nov 2009, 19:54
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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Re: Square patio with walkway [#permalink] New post   22 Nov 2009, 21:27
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One other way to solve this is that 132 meters is the size of the walkway. If we add the area of the patio inside it, then we know that the entire thing is still square and the area must be a perfect square.

132 + x = perfect square.

12 = 144
13 = 169
14 = 196
15 = 225

Lets see if any of the answers even result in a perfect square:

a) 56 + 132 = 188 [Not perfect square ]
b) 64 + 132 = 196 [Perfect square]
c) 68 + 132 = 200 [Not Perfect Square]
d) 81 + 132 = 213 [Not Perfect Square]
e) 100 + 132 = 232 [Not perfect square]

The only possibility is B
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Re: Square patio with walkway [#permalink] New post   22 Nov 2009, 20:34
Two equations can be formed from the question stem

1---- (a+2x)^2-a^2=132 => 4 x^2+4 a x132
2-----a=x+5

where a= width of the patio
x= width of the walk way

Solving we get a=8 and x=3

So the area of patio is 64
Hence the answer should be B
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Re: Square patio with walkway [#permalink] New post   22 Nov 2009, 20:45
Area of patio & walkway together = area of walkway + area of patio
\((3x+5)^2 = 132 + (x+5)^2\)
\((3x+5)^2 - (x+5)^2 = 132\)
\(8x^2+20x=132\)
\(x(2x+5) = 33 = 3*11\)
so \(x=3\)

area of patio is \((x+5)^2= 8^2 = 64\)

Answer B
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Re: Square patio with walkway [#permalink] New post   23 Nov 2009, 12:48
jallen morris, that's a much easier way to solve this. Thanks for advice.
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Re: Square patio with walkway [#permalink] New post   23 Nov 2009, 12:57
This scenario was easy because only one of the answers resulted in a perfect square, so the others were eliminated. If you would have come up with 2 answers that were perfect squares, such as 196 and 225, then you'd have to look further.

The number added to 132 resulting in 196 or 225 would have to be a perfect square as well because we're told the interior patio is square. From that standpoint, 64, 81 and 100 were options, but only 64 + 132 = a perfect square (196 = 14^2)

vannbj wrote:
jallen morris, that's a much easier way to solve this. Thanks for advice.




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Re: Square patio with walkway [#permalink]
23 Nov 2009, 12:57
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