The figure above represents an L-shaped garden

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

2 Explanations

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Aalam Singh Cheema

Hi the quadratic equation above has two values k=9 and k=21. Therefore should'nt (A) be insufficient? Thus answer would be (E)

All I can think where my approach went wrong was when I tried to plug k=21 for sides 15-k, they came out negative. So is that the only point i was missing? Thanks!

Aug 29, 2018 • Comment

Sam Kinsman, Magoosh Tutor

Hi Aalam, yes - that's right. If we use k=21, the sides (15-k) will be negative, and that's not possible. So only k=9 works.

You can also see that k=21 doesn't work by looking at the diagram. Notice that it's clear from the image that k must be shorter than 15. If k is longer, the diagram would not make sense.

I hope that helps!

Aug 30, 2018 • Reply

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Jordan Song

Statement (1)
The area of the garden, if it were a square, would be 225 sf. The area of the L-shaped garden is 189 sq. ft
Big square minus Small square equal to L-shape Garden = 189sf
225 - (15-k)(15-k) = 189sf
one equation, one variable - able to solve k
SUFFICIENT

Statement (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

Answer is A.

Apr 29, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Thanks for being an active member of the forum! And good job with this question :)

Apr 30, 2016 • Reply