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# If segment BD has a measure of x which of the following expresses the

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
If segment BD has a measure of x which of the following expresses the  [#permalink]

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13 Sep 2018, 04:39
00:00

Difficulty:

25% (medium)

Question Stats:

80% (03:01) correct 20% (01:50) wrong based on 26 sessions

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If segment BD has a measure of x which of the following expresses the perimeter of the triangle ABC in terms of x?

A. $$6x + 2x\sqrt{3}$$

B. $$6x + \frac{2x\sqrt{3}}{3}$$

C. $$4x + 4x\sqrt{3}$$

D. $$3x + x\sqrt{3}$$

E. $$2x + 2x\sqrt{3}$$

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Re: If segment BD has a measure of x which of the following expresses the  [#permalink]

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15 Sep 2018, 01:05
There are two 30 - 60 - 90 Triangles ABC and DBC -> ratio of the corresponding sides = a : a√3 : 2a

In triangle DBC ;
Opposite 60 BD =a√3= x (given)
Opposite 30 DC =a= x/√3
Opposite 90 BC =2a= 2x/√3 ,

In triangle ABC;
Opposite 30 bc=a = 2x/√3
opposite 90 ac= 2a= (4x/√3)
Opposite 60 ab=a√3=(2x/√3)√3 = 2x

Perimeter = ab+bc+ac =2x/√3 + (4x/√3) + 2x = 2x+2x√3 = ans E
Re: If segment BD has a measure of x which of the following expresses the   [#permalink] 15 Sep 2018, 01:05
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