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# The figure above represents a square plot measuring x feet o

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

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Updated on: 26 Sep 2013, 02:55
3
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84% (02:04) correct 16% (03:09) wrong based on 220 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, 02:52.
Last edited by Bunuel on 26 Sep 2013, 02:55, edited 1 time in total.
Edited the question.
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Joined: 02 Sep 2009
Posts: 51067
Re: The figure above represents a square plot measuring x feet o  [#permalink]

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26 Sep 2013, 02:56
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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).

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

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15 Apr 2014, 23:13
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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Re: The figure above represents a square plot measuring x feet o  [#permalink]

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16 Apr 2014, 00:07
1
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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31 Jul 2015, 07:10
1
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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16 Apr 2016, 06:27
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).

Answer: C.

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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Posts: 51067
Re: The figure above represents a square plot measuring x feet o  [#permalink]

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16 Apr 2016, 09:19
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).

Answer: C.

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 1901 times ]

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

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17 Apr 2016, 03:42
square root of 48 is approx. 6.9. Add 6 to that (2*3feet) and you get approximately 12.9... ?
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The figure above represents a square plot measuring x feet o  [#permalink]

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12 Jul 2017, 18:18
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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02 Dec 2018, 20:08
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# The figure above represents a square plot measuring x feet o

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