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Director  Joined: 29 Nov 2012
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The figure above represents a square plot measuring x feet o  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 78% (02:42) correct 22% (02:57) wrong based on 225 sessions

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The figure above represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walkway that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of X?

a) 8
b) 10
C) 12
d) 16
e) 18

Originally posted by fozzzy on 26 Sep 2013, 03:52.
Last edited by Bunuel on 26 Sep 2013, 03:55, edited 1 time in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 58453
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fozzzy wrote: The figure above represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walkway that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of X?

a) 8
b) 10
C) 12
d) 16
e) 18

The length of the rectangular garden would be $$x-2*2$$ and the width would be $$x-2*3$$ --> $$area=(x-4)(x-6)=48$$ --> $$x^2-10x-24=0$$ --> $$x=12$$ or $$x=-2$$ (not a valid solution).

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Manager  B
Joined: 10 Mar 2014
Posts: 180
Re: The figure above represents a square plot measuring x feet o  [#permalink]

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HI Bunnel,

If I will resolve the equation

x^2-10x-24=0 as x^2-4x-6x-24 = 0

then I will get x as 6,4

so value of x can be 6+3+3 or 6+2+2

12 or 10. both are present in the answer.
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Concentration: General Management, Strategy
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Re: The figure above represents a square plot measuring x feet o  [#permalink]

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PathFinder007 wrote:
HI Bunnel,

If I will resolve the equation

x^2-10x-24=0 as x^2-4x-6x-24 = 0

then I will get x as 6,4

so value of x can be 6+3+3 or 6+2+2

12 or 10. both are present in the answer.

Hi,

x^2-10x-24=0 can not be resolved as x^2-4x-6x-24 = 0 because multilpying your roots -4 and -6 will give 24, whereas the actual product in the equation is -24.

Hence the correct way to resolve this equation is this : x^2 -12x + 2x - 24 = 0
=> x(x-12) + 2 (x-12)=0 => (x + 2) (x - 12) = 0.

This gives 12 and -2 as the roots of the equation. Since the length can not be negative, the correct answer is 12.

Hope this helps.
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Re: The figure above represents a square plot measuring x feet o  [#permalink]

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fozzzy wrote:
Attachment:
image.jpg
The figure above represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walkway that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of X?

a) 8
b) 10
C) 12
d) 16
e) 18

the area of rectangular is 48 sqft, so the length and width could be 8 and 6
6 ft + 2*3 ft = 8 ft + 2*2 ft = 12 ft
ans c) 12 feet
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Re: The figure above represents a square plot measuring x feet o  [#permalink]

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Bunuel wrote:
fozzzy wrote: The figure above represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walkway that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of X?

a) 8
b) 10
C) 12
d) 16
e) 18

The length of the rectangular garden would be $$x-2*2$$ and the width would be $$x-2*3$$ --> $$area=(x-4)(x-6)=48$$ --> $$x^2-10x-24=0$$ --> $$x=12$$ or $$x=-2$$ (not a valid solution).

Hi Bunuel, how did you take the length as x-2*2 and breadth as x-2*3 ? I'm not able to figure out the reasoning behind this logic.
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Joined: 02 Sep 2009
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RaghavSingla wrote:
Bunuel wrote:
fozzzy wrote: The figure above represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walkway that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of X?

a) 8
b) 10
C) 12
d) 16
e) 18

The length of the rectangular garden would be $$x-2*2$$ and the width would be $$x-2*3$$ --> $$area=(x-4)(x-6)=48$$ --> $$x^2-10x-24=0$$ --> $$x=12$$ or $$x=-2$$ (not a valid solution).

Hi Bunuel, how did you take the length as x-2*2 and breadth as x-2*3 ? I'm not able to figure out the reasoning behind this logic.

Check below: The length= x - 2 -2 = x - 2*2
The width = x - 3 - 3 = x - 2*3

Attachment: Untitled.png [ 11.16 KiB | Viewed 3235 times ]

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Re: The figure above represents a square plot measuring x feet o  [#permalink]

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square root of 48 is approx. 6.9. Add 6 to that (2*3feet) and you get approximately 12.9... ?
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Joined: 22 May 2016
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The figure above represents a square plot measuring x feet o  [#permalink]

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fozzzy wrote:
Attachment:
image.jpg
The figure above represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walkway that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of X?

a) 8
b) 10
C) 12
d) 16
e) 18

Work from the answer choices. I'll pretend I started with E.

If x = 18, the length of the rectangle must be 18 - 2 - 2 (for each part of the walkway) = 14

OR 18 - 3 - 3 = 12 is the length of the rectangle.

Work with 12; it's a factor of 48, the area of the rectangle.

If rectangle length = 12, width is 48/12 = 4.

But that's the side that has 2-foot wide walkways.

Adding both 2-foot walkway parts to the width of the rectangle should yield 18.

4 + 2 + 2 = 8. Not possible. The outside shape is a square. Sides must be equal. 18 and 8 aren't equal.

No need to test rectangle length or width of 14. If 18 were the answer, because the outside is a square, it would yield 18 after taking walkway into account no matter which measure of rectangle side were used.

Try C, x = 12. If so, length of rectangle is 12 - 2 - 2 = 8. (Or 12 - 3 - 3 = 6.)

Work with L=8. If so, rectangle width must be 48/8 = 6.

When calculating rectangle length = 8, we accounted for the two 2-foot wide walkway parts.

So to rectangle width of 6, add the two 3-foot parts of the walkway: 3 + 3 = 6.

6 + 6 = 12, which is the number we need to make the sides be equal.

Answer C (which I chose to test first - got lucky)
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Senior Manager  P
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The figure above represents a square plot measuring x feet o  [#permalink]

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Algebra:
Area small rectangle: l*w = 48
Area big square: x² = (l+6)(w+4), since it's a square, l+6 = w+4 --> l+2 = w
Now we can solve the first equation:
l*(l+2) = 48
l²+2l-48 = 0
(l+8)(l-6) = 0
l = 6, -8
Thus, w = 8
Area is l+6 or w+4, so 6+6 or 8+4 = 12

Choose middle answer C), if x = 12 then 2 sides of rectangle are 12-6=6 & 12-4=8
Area is l*w = 48, testing 8*6 = 48, so this is our answer.
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Re: The figure above represents a square plot measuring x feet o  [#permalink]

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fozzzy wrote:
Attachment:
image.jpg
The figure above represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walkway that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of X?

a) 8
b) 10
C) 12
d) 16
e) 18

One side of the garden is x - 3 - 3 = x - 6, and the other side is x - 2 - 2 = x - 4. Therefore, we have:

(x - 6)(x - 4) = 48

x^2 - 10x + 24 = 48

x^2 - 10x - 24 = 0

(x - 12)(x + 2) = 0

x = 12 or x = -2

Since x can’t be negative, x = 12.

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Re: The figure above represents a square plot measuring x feet o  [#permalink]

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fozzzy wrote:
Attachment:
image.jpg
The figure above represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walkway that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of X?

a) 8
b) 10
C) 12
d) 16
e) 18

given: rectangle area is ab=48, and walkway is 3 wide on two opposite sides and 2 on the other two sides
then: rectangle area is ab=(x-3(2))(x-2(2))=48… xˆ2-6x-4x+24=48… xˆ2-10x-24=0… (x-12)(x+2)=0
since: x must be positive, then x=12 Re: The figure above represents a square plot measuring x feet o   [#permalink] 08 Jul 2019, 05:43
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