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The figure above represents an L-shaped garden. What is the value of k

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The figure above represents an L-shaped garden. What is the value of k [#permalink]

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The figure above represents an L-shaped garden. What is the value of k?

(1) The area of the garden is 189 square feet.
(2) The perimeter of the garden is 60 feet.


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[Reveal] Spoiler:
Attachment:
2015-10-26_2054.png
2015-10-26_2054.png [ 4.57 KiB | Viewed 9986 times ]
[Reveal] Spoiler: OA

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Re: The figure above represents an L-shaped garden. What is the value of k [#permalink]

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New post 27 Oct 2015, 13:15
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Bunuel wrote:
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The figure above represents an L-shaped garden. What is the value of k?

(1) The area of the garden is 189 square feet.
(2) The perimeter of the garden is 60 feet.


Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-26_2054.png



Stmt (1) - The area of the garden, if it were a square, would be 225 sq ft. The area of the L-shaped garden is 189 sq. ft - which is 36 sq ft less than a 15 x 15 square. Additionally, the missing piece is also a square and we can conclude that its dimensions are 6 x 6. The value of k is therefore 15 - 6, or 9. SUFFICIENT

Stmt (2) The perimeter of the garden will be 60 regardless of the value of k. For example, if k =5, the garden would have dimensions of 15, 5, 10, 10, 5 and 15 (total of 60). If k = 6, the garden's dimensions would be 15, 6, 9, 9, 6 and 15 (again total of 60). NOT SUFFICIENT

Answer is A.
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Re: The figure above represents an L-shaped garden. What is the value of k [#permalink]

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New post 26 Jun 2016, 12:01
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Bunuel wrote:
Image
The figure above represents an L-shaped garden. What is the value of k?

(1) The area of the garden is 189 square feet.
(2) The perimeter of the garden is 60 feet.


Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-26_2054.png


Statement 1. Area=15k+(15-k)k=189 Hence 30k-(k^2)=189 ==> (-k^2)+30k-189=0 D=b^2 - 4ac= 900 - 4(-1)(-189)=144 Hence k=(-30 +12)/(-2)=9 or k= (-30-12)(-2)=21 But k<15 hence k=9 Sufficient
Statement 2. Perimeter = 15+15+2k+(15-k) + (15-k)=60 ==> 60=60 k is eliminated Hence statement 2 is not sufficient

Answer A
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Re: The figure above represents an L-shaped garden. What is the value of k [#permalink]

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New post 06 Aug 2016, 04:42
Can someone please explain me this question in detail step by step. How could we assume the missing the piece as square ?

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Re: The figure above represents an L-shaped garden. What is the value of k [#permalink]

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New post 08 Aug 2016, 07:43
santro789 wrote:
Can someone please explain me this question in detail step by step. How could we assume the missing the piece as square ?



Santro,

The lengths of the two complete sides are 15 while the lengths of the two smaller sides are both k. If you imagine a square with sides of 15, then you can (hopefully) see that the missing piece has two sides that are 15 - k in length. Now, looking at the measure of the angles, we can also see that this missing piece has all 90 degree angles. Thus, it is either a rectangle or square. But, since the top piece is 15- k in length and the left side piece is 15 - k in length AND they are both parallel to the sides opposite them, we can conclude that the missing piece is also a square.

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Re: The figure above represents an L-shaped garden. What is the value of k [#permalink]

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Re: The figure above represents an L-shaped garden. What is the value of k   [#permalink] 19 Aug 2017, 03:53
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