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# If in the figure above XY = YZ, what is the length of XZ?

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
If in the figure above XY = YZ, what is the length of XZ?  [#permalink]

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29 Aug 2018, 02:17
00:00

Difficulty:

15% (low)

Question Stats:

82% (00:50) correct 18% (01:22) wrong based on 43 sessions

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NOTE: Figure not drawn to scale

If in the figure above XY = YZ, what is the length of XZ?

(1) $$XY = 2\sqrt{3}$$

(2) $$XY + YZ= 4\sqrt{3}$$

Attachment:

image009.jpg [ 3.5 KiB | Viewed 516 times ]

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Re: If in the figure above XY = YZ, what is the length of XZ?  [#permalink]

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29 Aug 2018, 02:50
Bunuel wrote:

NOTE: Figure not drawn to scale

If in the figure above XY = YZ, what is the length of XZ?

(1) $$XY = 2\sqrt{3}$$

(2) $$XY + YZ= 4\sqrt{3}$$

Attachment:
image009.jpg
St1)
Assume that the figure is restricted now with fixed length of XY and YZ at a fixed angle. So this condition holds true for only one value of side XZ. ( can't increase or decrease under the given restriction)

Sufficient

St2) since xy =yz
It means both have a defined length at a particular angle. We can't stretch XZ with given restriction neither shrink it. No need to calculate the value.

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Re: If in the figure above XY = YZ, what is the length of XZ?  [#permalink]

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29 Aug 2018, 05:20
1
XY = YZ, makes it an isosceles triangle
Angle X = Angle Z = 45
Angle Y = 90
Now the triangle above is isosceles right triangle, we can find XZ by using pythagoras theorem

(1) XY = 2√3
Angle known, alternate side known, apply pythagoras theorem
Sufficient

(2) XY + YZ = 4√3
2XY = 4√3 or 2YZ = 4√3
XY = 2√3 or YZ = 2√3
Angle known, alternate side known, apply pythagoras theorem
Sufficient

Hence, D.
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Re: If in the figure above XY = YZ, what is the length of XZ?   [#permalink] 29 Aug 2018, 05:20
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