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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The figure above represents an L-shaped garden. What is the value of k

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

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Difficulty:   95% (hard)

Question Stats: 47% (02:11) correct 53% (02:03) wrong based on 2280 sessions

### HideShow timer Statistics 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 [ 4.57 KiB | Viewed 34036 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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Bunuel wrote: 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

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

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Bunuel wrote: 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

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

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

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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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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).

(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  [#permalink]

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why the article before "L-shaped garden" is "an" but not "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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alienetie1217 wrote:
why the article before "L-shaped garden" is "an" but not "a"?

Hi alienetie1217,

The pronunciation of "L-shaped" is "ehl' NOT 'll'. Hence it starts with "AN" NOT "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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Top Contributor
Bunuel wrote: 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.
Attachment:
2015-10-26_2054.png

Target question: What is the value of k?

Statement 1: The area of the garden is 189 square feet.
Let's drawn an auxiliary line that divides the shape into two rectangular regions A and B. Regions A and B have the following measurements. So, the area of region A = k(15 - k) = 15k - k²
The area of region B = 15k
So, the TOTAL area = 15k - k² + 15k = 30k - k²

Since we're told the area is 189, we can write: 30k - k² = 189
Rearrange to get: k² - 30k + 189 = 0
Factor: (k - 21)(k - 9) = 0
So, EITHER k = 21 OR k = 9

HOLD ON!
k cannot be greater than 15 (since one entire side has length 15)
So, it MUST be the case that k = 9
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The perimeter of the garden is 60 feet.
This statement provides NO NEW information, because the perimeter will ALWAYS be 60, regardless of the value of k.
Here's why:
If k = the two given sides, then the remaining two sides must both have a length of 15 - k So, when we add all lengths, we get: PERIMETER = k + (15 - k) + (15 - k) + k + 15 + 15 = 60

If you're not convinced, consider these two possible cases:

Case a: Notice that the perimeter = 60
In this case, the answer to the target question is k = 6

Case b: Notice that the perimeter = 60
In this case, the answer to the target question is k = 5

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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Bunuel wrote: 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

1) 225 - 189 = (15 - k)^2
6 = 15 - k
k = 9 => Sufficient

2) 15 + 15 + 15 -k + 15 -k + 2k = 60
60 = 60 => Not Sufficient

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

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VeritasPrepDennis wrote:
Bunuel wrote: 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

How can we conclude that the missing piece is a square?

I used the following equation=>
=(15-k)*k=36=> k=3 or 12
Both are viable answers so I couldnt prove this was sufficient. What did i get wrong?
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Re: The figure above represents an L-shaped garden. What is the value of k  [#permalink]

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livfcind wrote:
VeritasPrepDennis wrote:
Bunuel wrote: 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

How can we conclude that the missing piece is a square?

I used the following equation=>
=(15-k)*k=36=> k=3 or 12
Both are viable answers so I couldnt prove this was sufficient. What did i get wrong?

Hi livfcind,

To start, there's an error in your equation. The two dimensions of the "missing upper-left corner" are BOTH (15 - K) and since we are clearly dealing with 90-degree angles, that 'corner' would have to be a square.

Based on the information in Fact 1, if you want to create an equation that will account for the "missing upper-left corner" of the picture, then the equation would be...

(15 - K)(15 - K) = 36
(15 - K)^2 = 36

So, what numbers, when 'squared', equal 36? The answer is +6 or -6 (but since we're dealing with a geometric shape, we can't have a "negative length", so that corner is a 6x6 square and the value of K must be 9.

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_________________ Re: The figure above represents an L-shaped garden. What is the value of k   [#permalink] 30 May 2020, 10:48

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