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# If the area of the above triangle is 8*3^(1/2), what is the length of

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Joined: 02 Sep 2009
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If the area of the above triangle is 8*3^(1/2), what is the length of  [#permalink]

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14 Mar 2019, 00:02
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Difficulty:

25% (medium)

Question Stats:

79% (01:38) correct 21% (01:47) wrong based on 28 sessions

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If the area of the above triangle is $$8\sqrt{3}$$, what is the length of side AB?

A. 3
B. 4
C. $$4\sqrt{3}$$
D. $$6\sqrt{3}$$
E. $$8\sqrt{3}$$

Attachment:

trid14.png [ 6.33 KiB | Viewed 386 times ]

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Re: If the area of the above triangle is 8*3^(1/2), what is the length of  [#permalink]

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14 Mar 2019, 00:24
the triangle is 60-30-90 right angled triangled.

Hence- AB:AC:BC = 1:\sqrt{3}:2

if AB= x and AC = \sqrt{3}x

1/2*\sqrt{3}*x^2 = 8\sqrt{3}

=> x^2 = 16
=> x = 4

So AB=4 So correct ans B
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Re: If the area of the above triangle is 8*3^(1/2), what is the length of  [#permalink]

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14 Mar 2019, 03:59
Bunuel wrote:

If the area of the above triangle is $$8\sqrt{3}$$, what is the length of side AB?

A. 3
B. 4
C. $$4\sqrt{3}$$
D. $$6\sqrt{3}$$
E. $$8\sqrt{3}$$

Attachment:
trid14.png

30:60:90
x:x√2:2x
so
1/2* x*x√3= 8√3
solve for x
x= 4
IMO B
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Re: If the area of the above triangle is 8*3^(1/2), what is the length of  [#permalink]

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18 Mar 2019, 18:47
Bunuel wrote:

If the area of the above triangle is $$8\sqrt{3}$$, what is the length of side AB?

A. 3
B. 4
C. $$4\sqrt{3}$$
D. $$6\sqrt{3}$$
E. $$8\sqrt{3}$$

Attachment:
trid14.png

We have a 30-60-90 right triangle. If we let the length of AB = x, then the length of AC = x√3 and we can create the following equation for the area of the triangle:

8√3 = (x)(x√3)/2

16√3 = (x)(x√3)

16 = x^2

4 = x

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Re: If the area of the above triangle is 8*3^(1/2), what is the length of   [#permalink] 18 Mar 2019, 18:47
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