SOLUTION: the largest side of a triangle is twice the smallest and the largest angle thrice the smallest. the area of the triangle is 32sqrt(3). What is the length of the largest side
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Question 550578: the largest side of a triangle is twice the smallest and the largest angle thrice the smallest. the area of the triangle is 32sqrt(3). What is the length of the largest side
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The largest side being twice the smallest makes the triangle a candidate to be a 30-60-90 right triangle. The largest angle being thrice the smallest clinches it: 90 is three times 30.
The sides of a 30-60-90 right triangle are in proportion 
. Since it is a right triangle, one of the legs is the base and the other leg is the altitude. Hence, a 30-60-90 right triangle with a hypotenuse of 1 would have an area of 
.
So
\ =\ 32\sqrt{3})
Solve for 
John
My calculator said it, I believe it, that settles it
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