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

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

11 Dec 2008, 16:21

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

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Re: patio [#permalink]

11 Dec 2008, 17:48

haichao wrote:

Can you please check the q -

backworking will be easier and faster for this question -

Lets start with E
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 :-D

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Re: patio [#permalink]

12 Dec 2008, 15:04

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, 15:04

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

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

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

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