gmatter2012 wrote:In the Triangle shown in the figure what is the value of x ?
Since the figure includes a 30 degree angle, draw a 30-60-90 triangle:
The sides of a 30-60-90 triangle are proportioned s : s√3 : 2s.
Thus, BD = x/2 and DC = (x√3)/2.
We can plug in the answers, which represent the value of x.
The figure indicates that BD<√2.
Eliminate C, D and E, which will yield too great a value for BD.
Since a 30-60-90 triangle includes a side of √3, the correct answer is likely to be B.
Answer choice B: 1 + √3
BD = x/2 = (1+√3)/2
DC = (x√3)/2 = (1+√3)(√3) / 2 = (√3+3)/2.
AD = x - DC = (1+√3) - (√3+3)/2 = (2 + 2√3 - √3 - 3) / 2 = (√3-1)/2.
For B to be correct, AD² + BD² = AB²:
(√3-1)² / 2² + (1+√3)² / 2² = (√2)²
(3 - 2√3 + 1)/4 + (1 + 2√3 + 3)/4 = 2
8/4 = 2
2=2.
Success!
The correct answer is
B.
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