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The figure shows a square patio surrounded by a walkway of [#permalink]
24 Oct 2008, 02:46

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The figure shows 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: PS : SQUARE PATIO [#permalink]
30 Dec 2008, 09:17

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Hi LiveStronger, nice way to solve it. could you please explain me how do you go from step 1 to step 2. It took me 3 lines of operations and you can do it in just one. I definitely need to be faster in the exam so this kind of tips will be really useful. thks!!

Re: PS : SQUARE PATIO [#permalink]
30 Dec 2008, 09:38

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This post received KUDOS

marcap wrote:

Hi LiveStronger, nice way to solve it. could you please explain me how do you go from step 1 to step 2. It took me 3 lines of operations and you can do it in just one. I definitely need to be faster in the exam so this kind of tips will be really useful. thks!!

Re: PS : SQUARE PATIO [#permalink]
30 Dec 2008, 10:35

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This post received KUDOS

The solutions above subtract the inner square from the outer one, which is a good approach. One other way to get to the same answer: divide up the patio. You have the four corners, measuring x by x, and four rectangles lined up with each side of the inner square which measure x by x+5. So:

4x^2 + 4x(x+5) = 132 2x^2 + 5x = 33

etc. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: PS : SQUARE PATIO [#permalink]
30 Dec 2008, 11:13

amitdgr wrote:

The figure shows 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

width of the walkway = x width of the patio = x+5 = x+5 width of the whole area = x+5+x = 3x+5

(3x+5)^2 - (x+5)^2 = 132 9x^2 + 30x + 25 - x^2 -10x -25 = 132 8x^2 + 20x = 132 4 (2x^2 + 5x) = 132 2x^2 + 5x - 33 = 0 2x^2 + 11x - 6x - 33 = 0 x (2x+11) -3 (3x +11) = 0 (x-3) (2x+11) = 0 x = 3 or -11/2 but -11/2 is not possible as length/width cannot be in -ve. so x = 30

so area of the patio = (3+5)^2 = 64 _________________

Re: PS : SQUARE PATIO [#permalink]
30 Dec 2008, 22:38

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If its convenient, u can also attempt backsolving it:- On first glance A,C are clearly out. (E) 100 means side of patio is 10 so width of walkway =5. the walkway has 4 rectangles 2 among them are each 20*5=100 --impossible for total of 132. (D) 81 means side of patio is 9 so width of walkway =4. the walkway has 4 rectangles 2 among them are each 17*4=68. 2 such rectangles account for 136--hence impossible for total of 132. (C) 64 means side of patio is 8 so width of walkway =3. the walkway has 4 rectangles 2 among them are each 14*3=42 and rest are 8*24.total= 2(42+24)=132.

Re: PS : SQUARE PATIO [#permalink]
25 Aug 2011, 22:22

amitdgr wrote:

The figure shows 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

Smaller square=Patio Let the side of Patio be "s". Width of walkway=x width of the patio is 5 meters greater than the width of the walkway(Actually it should be "side of the patio is 5 meters greater than the width of the walkway" because patio is a square)

So, s=x+5

If we see the figure properly, the outer quadrilateral is also a square with side s+x+x OR x+5+x+x=3x+5

We know, the area of the walkway is 132 square meters:

Area of walkway=Area of outer square-Area of inner square Area of walkway=(3x+5)^2-(x+5)^2=132