SOLUTION: What is the lenth of the smallest side of a triangle if the measures of the angles are in ratio 1:2:3, and the perimeter is 30 + 10√3? ~The only answer choice I have is 10

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Question 979366: What is the lenth of the smallest side of a triangle if the measures of the angles are in ratio 1:2:3, and the perimeter is 30 + 10√3?
~The only answer choice I have is 10 or 20. I have tried but with both attempts, I got it wrong. Please help!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If the angles are in a ratio of 1%3A2%3A3, then let x+ be smallest angle.

The other angles are 2x+and 3x respectively, so
x+%2B+2x+%2B+3x=180
6x=180
x=30
2x=60
3x=90
x=30

so, this is a 30-60-90 triangle, so the sides are in a ratio of 1%3A2%3Asqrt%283%29.

Let
y be first side
2y second side (hypotenuse of right triangle)
y%2Asqrt%283%29 third side

Perimeter
+P=y%2B+2y+%2B+y%2Asqrt%283%29=30%2B10%2Asqrt%283%29
3y%2B+y%2Asqrt%283%29+=+30%2B+10%2Asqrt%283%29

Therefore, y=10.
the smallest side is highlight%2810%29,
the second side is 20, and
the third side is 10%2Asqrt%283%29