by: Sajjad1994
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angles in ratio x:2x:3x so its a 30-60-90 triangle and with shortest side 1, from trigonometry we have hypotenuse =2 and longest side =\sqrt{3},
so area =1/2 * base * height
= 1/2 * 1 *\sqrt{3}
= \sqrt{3}/2 which is D
so area =1/2 * base * height
= 1/2 * 1 *\sqrt{3}
= \sqrt{3}/2 which is D
x+2x+3x=180
x=180/6, x=30
so the angles are 30,60,90
and AB is the shortest side and it has to be oppsite to 30.
in 30-60-90 combination the ratio of lengths are 1:\sqrt{3}:2
so the one opp to 60 is \sqrt{3}
one opp to 90 is 2
the area is \sqrt{3}
x=180/6, x=30
so the angles are 30,60,90
and AB is the shortest side and it has to be oppsite to 30.
in 30-60-90 combination the ratio of lengths are 1:\sqrt{3}:2
so the one opp to 60 is \sqrt{3}
one opp to 90 is 2
the area is \sqrt{3}
divyakatas
kirankp has it right and you are very close, something wrong in the final step...
OA:
\(x+2x+3x=180\) --> \(x=30\) degrees, \(2x=60\) degrees, \(3x=90\) degrees.
Hence we have right triangle \(30-60-90\) and the shortest side\(=1\).
For the right triangle \(30-60-90\) the ratio of sides are \(1/\sqrt{3}/2\), as the shortest side is \(1\): \(Area=1*\sqrt{3}/2=\sqrt{3}/2\)
Answer: D.
_________________
Hence we have right triangle \(30-60-90\) and the shortest side\(=1\).
For the right triangle \(30-60-90\) the ratio of sides are \(1/\sqrt{3}/2\), as the shortest side is \(1\): \(Area=1*\sqrt{3}/2=\sqrt{3}/2\)
Answer: D.
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