SOLUTION: the lengths of two sides of an obtuse triangle are 12 and 16. which could NOT be the length of the third side? F 9 G 10 H 20 J 25

Question 389499: the lengths of two sides of an obtuse triangle are 12 and 16. which could NOT be the length of the third side?
F 9
G 10
H 20
J 25
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
A triangle is obtuse if and only if, the sum of the squares of the shortest two sides is shorter than the square of the third side (this follows from the law of cosines).

Now we just plug in numbers and check:

9^2 + 12^2 < 16^2
10^2 + 12^2 < 16^2
12^2 + 16^2 = 20^2
12^2 + 16^2 < 25^2

The answer is 20 (this creates a right triangle).
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