SOLUTION: If the measures of the angles of a triangle are in the ratio of 1:2:3, and if the perimeter of the triangle is 30+10√3, what is the length of the smallest side?
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Question 1104582: If the measures of the angles of a triangle are in the ratio of 1:2:3, and if the perimeter of the triangle is 30+10√3, what is the length of the smallest side? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! If the measures of the angles of a triangle are in the ratio of 1:2:3, and if the perimeter of the triangle is 30+10√3, what is the length of the smallest side?
Angles:: x + 2x + 3x = 180
6x = 180
x = 30 degrees (smallest angle)
2x = 60 degrees and 3x = 90 degrees
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So the sides are in the ratio of 1:2:Sqrt(3)
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Equation:
x + 2x + sqrt(3)x = 30+10sqrt(3)
3x + sqrt(3)x = 30+10sqrt(3)
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So, x = 10 (That is the length of the smallest side)
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Cheers,
Stan H.
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