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What is the perimeter of right triangle ABC above?

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What is the perimeter of right triangle ABC above? [#permalink] New post   20 Sep 2018, 17:03
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What is the perimeter of right triangle ABC above?
(A) \(6 + 4\sqrt{3}\)
(B) \(6 + 6\sqrt{3}\)
(C) \(6 + 8\sqrt{3}\)
(D) \(9 + 6\sqrt{3}\)
(E) \(18 + 6\sqrt{3}\)
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Re: What is the perimeter of right triangle ABC above? [#permalink] New post   25 Sep 2018, 20:10
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the given triangle is in 30-60-90 format
side opposite 60 degree has length 6.
In a 30-60-90 triangle sides are in the ratio \(x,x\sqrt{3},2x\)
therefore, \(x\sqrt{3}=6\)
solving for x we get \(x=\frac{6}{\sqrt{3}}=2\sqrt{3}\)
the third side is \(4\sqrt{3}\)

Perimeter = \(6+4\sqrt{3}+2\sqrt{3} = 6+6\sqrt{3}\)
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Re: What is the perimeter of right triangle ABC above? [#permalink] New post   11 Sep 2021, 07:37
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Re: What is the perimeter of right triangle ABC above? [#permalink]
11 Sep 2021, 07:37
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