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# What is the area of Triangle XYZ?

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Math Expert
Joined: 02 Sep 2009
Posts: 50062
What is the area of Triangle XYZ?  [#permalink]

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16 Apr 2018, 05:05
00:00

Difficulty:

25% (medium)

Question Stats:

78% (00:52) correct 22% (01:05) wrong based on 49 sessions

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What is the area of Triangle XYZ?

A. 4√3
B. 8
C. 8√3
D. 16
E. 16√3

Attachment:

TriangleXYZ.png [ 6.66 KiB | Viewed 690 times ]

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Re: What is the area of Triangle XYZ?  [#permalink]

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16 Apr 2018, 08:32
[quote="Bunuel"]
What is the area of Triangle XYZ?

A. 4√3
B. 8
C. 8√3
D. 16
E. 16√3

XZ^2 = YZ^2 - XY^2

XZ^2 = 8^2 - 4^2

XZ^2 = 64 -16 = 48

XZ = √48 = √16 * √3 = 4√3

Area = 1/2 base * height = 1/2 * 4√3 * 4 = 8√3

Hence option C = 8√3 is the answer.
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What is the area of Triangle XYZ?  [#permalink]

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22 Apr 2018, 18:05
Bunuel wrote:

What is the area of Triangle XYZ?

A. 4√3
B. 8
C. 8√3
D. 16
E. 16√3

Attachment:
TriangleXYZ.png

Watch for special triangles, especially if you see $$\sqrt{3}$$ or $$\sqrt{2}$$ in answer choices.

Rule: A right triangle whose hypotenuse is twice the length of one of its legs is a 30-60-90 triangle

30-60-90 triangles have corresponding sides opposite those angles in ratio
$$x : x\sqrt{3}: 2x$$

$$2x$$
, opposite the 90° angle = $$8$$
$$x= 4$$

So the other leg, $$x\sqrt{3}=4\sqrt{3}$$

Area, $$A=\frac{b*h}{2}$$

$$A= \frac{4*4\sqrt{3}}{2}=8\sqrt{3}$$

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What is the area of Triangle XYZ? &nbs [#permalink] 22 Apr 2018, 18:05
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