Question 979369: What is the length 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 square root 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 Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
What is the length 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 square root 3?
~~The only answer choice I have is 10 or 20. I have tried but with both attempts, I got it wrong. Please help!
-------------------
If 10 or 20 is not the right answer, you have no control over that.
1x + 2x + 3x = 6x = 180 degrees
x = 30
--> angles of 30, 60 & 90 degs
--------------
For a 30-60-90 triangle:
If the shortest side length = 1, the hypotenuse = 2
The 3rd side = sqrt(2^2 - 1) = sqrt(3)
Perimeter = 3 + sqrt(3)
------
The perimeter you're given is 10 times that, and it's linearly related.
--> the shortest side's length = 10
|
|
|
