SOLUTION: Can we make a triangle with side lengths: 12, 18, and 16?

Algebra ->  Triangles -> SOLUTION: Can we make a triangle with side lengths: 12, 18, and 16?      Log On


   

Question 530511: Can we make a triangle with side lengths: 12, 18, and 16?
Found 2 solutions by reviewermath, oberobic:
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
highlight%28NO%29 because 18 - 12 = 6 and 18 + 12 = 30 The third side is between 6 and 30, exclusive. So 6 is not possible side if the other 2 sides are 12 and 18.

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Applying the law of cosines:
.
c^2 = a^2 + b^2 - 2*a*b*(cos(x)), where 'x' is the angle between 'a' and 'b'.
.
c^2 - a^2 - b^2 = -2*a*b*(cos(x))
.
(c^2 -a^2 -b^2)/(-2*a*b) = cos(x)
.
(18^2 -12^2 -16^2)/(-2*12*16) = .1979166666666667
.
We can see that .1979166666666667 is a valid value for the cosine function.
.
So, yes, you could have a triangle with sides of 12, 16, and 18.
.
Done.