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# a square patio surrounded by a walkway of width x meters. If

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Manager
Joined: 06 Nov 2008
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a square patio surrounded by a walkway of width x meters. If [#permalink]  11 Dec 2008, 15:21
a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

A. 56
B. 64
C. 68
D. 81
E. 100
Intern
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Re: patio [#permalink]  11 Dec 2008, 16:48
haichao wrote:
a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

A. 56
B. 64
C. 68
D. 81
E. 100

Can you please check the q -

backworking will be easier and faster for this question -

width of the patio is 10
width of the walkway is 5
width of the square including walkway is 15
width of the walkway is 15^2 - 10^2 = 125

Assuming that my assumptions are ok
Senior Manager
Joined: 30 Nov 2008
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Re: patio [#permalink]  12 Dec 2008, 14:04
My guess would be B = 64.

Let x be the width of the walkway. It is given that width of the pation is 5 greater than the width of the walkway. So patio width is x+5.

Area of the patio is (x+5) ^2.

Now the total length of the patio with walkway surrounded will be = length of the pation + 2 width of the patio (one on each side
= 3+5 +2x = 3x+5.

Area of the patio with Walkway suurended is (3x+5) ^ 2.

It is given that walk way area alone is 132.

So (3x + 5) ^ 2 - (x +5) ^2 = 132.
==> (4x+10)2x = 132 (applied (a+b)(a-b) = a^2 -b^2)
==> (2x+5)x = 33
==> x = 3

Length of the pation = x+ 5 = 8. Area is 8^2 = 64.
Re: patio   [#permalink] 12 Dec 2008, 14:04
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