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# The figure shows a square patio surrounded by a walkway of width x

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Manager
Joined: 13 Sep 2014
Posts: 86
WE: Engineering (Consulting)
Re: The figure shows a square patio surrounded by a walkway of width x  [#permalink]

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20 Jul 2015, 03:15
width of the walkway = x
width of the small square = x+5 = x+5
width of the whole large square = x+5+x+x = 3x+5

Difference between area
(3x+5)^2 - (x+5)^2 = 132
8x^2 +20x = 132
4x(2x+5) = 132
x (2x+5) = 33 = 3*11
Hence, x = 3
x+5 = 8
8^2 = 64
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Joined: 03 Jul 2015
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Re: The figure shows a square patio surrounded by a walkway of width x  [#permalink]

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14 Oct 2015, 06:23
Engr2012 wrote:
PathFinder007 wrote:
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

Hi bunuel,

i didnt get it.

Thanks.

It is given that width of the patio is 5 more than width of the walkway. Now, walkway's 'extension on either side of the patio' is 'x' and thus width of the of the patio = $$W_P$$ = 5+x

Now, total width of the walkway = $$W_W$$ = width of the patio + 2*x = 5+x+2x = 5+3x

it requires a redesign figure, which is not provided by anyone, only for this reason many confusion arise, could you please make a understandable figure please?
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Re: The figure shows a square patio surrounded by a walkway of width x  [#permalink]

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22 Oct 2016, 04:20
(3x+5)^2 - (x+5)^2 = 132

Solving for x = 64

Hence B
Manager
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Location: India
Re: The figure shows a square patio surrounded by a walkway of width x  [#permalink]

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18 Jul 2017, 23:11
I eventually didn't understand the figure . The outer box is the walkway and the inner one is the patio. Am i correct? Sorry seems like silly question, but iam weak in geometry and it would really great if someone could help me understand the figure.
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Posts: 64243
Re: The figure shows a square patio surrounded by a walkway of width x  [#permalink]

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19 Jul 2017, 00:03
longhaul123 wrote:
I eventually didn't understand the figure . The outer box is the walkway and the inner one is the patio. Am i correct? Sorry seems like silly question, but iam weak in geometry and it would really great if someone could help me understand the figure.

We are given that the patio is surrounded by a walkway, so yellow area is walkway and red is patio itself.
Attachment:

patio.JPG [ 13.39 KiB | Viewed 827 times ]

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Re: The figure shows a square patio surrounded by a walkway of width x  [#permalink]

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19 Jul 2017, 22:01
Thank youBunuel
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Joined: 20 Jul 2017
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Re: The figure shows a square patio surrounded by a walkway of width x  [#permalink]

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20 Jul 2017, 01:49
I did not realise this when I first read the question but with hindsight the fastest way to solve this is to realise that:

A) 56 not a square
B) 64 is ok and 64+132 =196 is also ok
C) 58 not a square
D) 81+132 = 213 not a square
E) 100+132 = 232 not a square

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Re: The figure shows a square patio surrounded by a walkway of width x  [#permalink]

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25 Jul 2017, 10:14
1

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

If we let x = the width of the walkway, then the width of the patio = x + 5. Let’s create the equation for the area of the combined walkway and patio. We see that the entire length of the combined walkway-patio is (x + x + x + 5) = (3x + 5). Because it is a square, we square (3x + 5) to determine the combined area. We see that this is equal to the area of the patio plus the area of the walkway:

(3x + 5)^2 = (x + 5)^2 + 132

9x^3 + 30x + 25 = x^2 + 10x + 25 + 132

8x^2 + 20x - 132 = 0

2x^2 + 5x - 33 = 0

(2x + 11)(x - 3) = 0

2x + 11 = 0

2x = -11

x = -5.5

Or x = 3

Since x cannot be negative, x = 3.

Since x = 3, the area of the patio is (3 + 5)^2 = 8^2 = 64.

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Re: The figure shows a square patio surrounded by a walkway of width x  [#permalink]

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07 Aug 2019, 21:39

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

Attachment:
patio.JPG

Leave everything else.
If I have to add something to 132 the result should be a perfect square. Option B works.
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Re: The figure shows a square patio surrounded by a walkway of width x  [#permalink]

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07 Aug 2019, 22:50
Since it is a square the area should be a perfect square.

Area given 132

Option b 64

Total area 64+132=196

Side =14

Only this option has a perfect square

Posted from my mobile device
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Re: The figure shows a square patio surrounded by a walkway of width x  [#permalink]

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07 Aug 2019, 23:09
Ans 64. Attached solution

Posted from my mobile device
Attachments

IMG_20190808_123756099.jpg [ 2.43 MiB | Viewed 141 times ]

Re: The figure shows a square patio surrounded by a walkway of width x   [#permalink] 07 Aug 2019, 23:09

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