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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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New post 26 Oct 2015, 09:55
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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.

Attachment:
2015-10-26_2054.png
2015-10-26_2054.png [ 4.57 KiB | Viewed 16161 times ]

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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:
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.

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.

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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New post 11 Dec 2017, 15:03
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Hi All,

We're asked for the value of K in the drawing. While we normally have to be careful about trusting a picture in a DS question, we can trust the data in the drawing. We know that all of the angles are right angles and we know that the L-shaped garden is essentially a big square with a small square-shaped corner removed (and the length of a side on that square is (15-K)).

1) The area of the garden is 189 square feet.

A 15ft x 15ft square would have an area of 225 sq. ft. Since the garden is 189 sq ft., we know the missing corner = 225 - 189 = 36 sq. ft. This means that each side of that little square would have to be 6. Thus, 15 - K = 6, so K = 9.
Fact 1 is SUFFICIENT

2) The perimeter of the garden is 60 feet.

With this Fact, we can create the following equation (where X is one of the unlabeled sides):
15 + 15 + K + K + X + X = 60
2K + 2X = 30
K + X = 15

This is NOT new information (we knew this from the prompt). Thus, K could be any value in the range of 0 < K < 15.
Fact 2 is INSUFFICIENT

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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 01 Jul 2018, 21:19
I reached the second option through algebraic approach, which returns the exact value of k=7.5
Sum of all sides = 3(15-k)+k+30= 60. Which reduces to k=7.5.
Could anyone please point out where I'm making mistake???

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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 02 Jul 2018, 05:10
Blackishmamba wrote:
I reached the second option through algebraic approach, which returns the exact value of k=7.5
Sum of all sides = 3(15-k)+k+30= 60. Which reduces to k=7.5.
Could anyone please point out where I'm making mistake???

Posted from my mobile device


The perimeter = 15 + 15 + k + k + (15 - k) + (15 - k) = 60. k's would cancel and you'd get 60 = 60.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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 Jul 2018, 14:47
Bunuel wrote:
Blackishmamba wrote:
I reached the second option through algebraic approach, which returns the exact value of k=7.5
Sum of all sides = 3(15-k)+k+30= 60. Which reduces to k=7.5.
Could anyone please point out where I'm making mistake???

Posted from my mobile device


The perimeter = 15 + 15 + k + k + (15 - k) + (15 - k) = 60. k's would cancel and you'd get 60 = 60.


Hi,

Can we solve this problem if we consider two rectangle areas: 15 x K (first) + K (15-K)(second) =189 ? , I tried with this but can´t get the solution.
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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 Jul 2018, 15:59
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Hi Omar31Peru,

Yes, you can deal with the information in Fact 1 by setting up a Quadratic equation (although it comes with a 'tweak' to the logic).

You can start with your equation and simplify as follows:

(15)(K) + (K)(15-K) = 189
15K + 15K - K^2 = 189
30K - K^2 = 189
0 = K^2 - 30K + 189
0 = (K-9)(K-21)
K = 9 or 21

Based on what we know about the garden, K CANNOT be 21, so the only possible value would be K=9. Thus, Fact 1 is SUFFICIENT.

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Re: The figure above represents an L-shaped garden. What is the value of k &nbs [#permalink] 26 Jul 2018, 15:59
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