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In the figure above, x, y, and z denote the lengths of the sides of a

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Bunuel
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In the figure above, x, y, and z denote the lengths of the sides of a [#permalink] New post   17 Dec 2014, 07:48
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In the figure above, x, y, and z denote the lengths of the sides of a triangular flower bed bounded by three driveways. What is the perimeter of the flower bed ?

(1) x = y = 30 feet.
(2) k = 60



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C
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uday1409
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Re: In the figure above, x, y, and z denote the lengths of the sides of a [#permalink] New post   17 Dec 2014, 08:39
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1. dont know z. Insufficeint

2. simply with one angle we cant determine . Insufficent,

1+2>> x=30;y=30 and angle opposite to x=60

so angle opposite to y also must be 60 because x and y are equal and form isoseles triangle.

we also have from triangle property angle opp to x+angleopp to y+angle opp to z=180
angle opp to z=180-60-60=60

three angles are equal so their lengths. hence z=30 ft

x+y+z=90 ft
Sufficeint

Ans C
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Re: In the figure above, x, y, and z denote the lengths of the sides of a [#permalink] New post   17 Dec 2014, 21:43
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Bunuel wrote:

Tough and Tricky questions: Geometry.




In the figure above, x, y, and z denote the lengths of the sides of a triangular flower bed bounded by three driveways. What is the perimeter of the flower bed ?

(1) x = y = 30 feet.
(2) k = 60


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We need to find x+y+z

St 1 says x=y=30....So this means 0<z<60...Third side is greater than the difference of other 2 sides and less than sum of other 2 sides
Not sufficient

St 2 says k=60 again not sufficient ...so angle between x and y is 60...not sufficient

Combining the 2 statements we get that x=y so 30 ft and k=60=angle between sides x and y...this means that it is equilateral triangle and perimeter =90
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Re: In the figure above, x, y, and z denote the lengths of the sides of a [#permalink] New post   17 Dec 2014, 23:51
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A gives no value about z so not suffice
B gives angle equal 60 so not suffice
Together triangle a is equilateral with side 30 so sufficient.
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Re: In the figure above, x, y, and z denote the lengths of the sides of a [#permalink] New post   20 Dec 2014, 10:48
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Solution: Determine x + y + z ?

Statement 1: x = y = 30 feet
Since we don't know z - Insufficient

Statement 2: k = 60
We don't know the length of each sides - Insufficient

Combining 1 & 2, Since k=60, angle opposite to side x=60 --(alternate angles)
angle opposite to side y=60 -- (x=y=30)
Also angle opposite z=60 -- sum of all three angles is 180
Thus length of z=30
Two statements together are sufficient, Answer C
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Re: In the figure above, x, y, and z denote the lengths of the sides of a [#permalink]
20 Dec 2014, 10:48
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Bunuel
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