Word problem:

The sides of a triangle have lengths x, x+4, and 20. Specify those values of x for which the triangle is acute with longest side 20.

The answer is 12 < x <= 16. However, I don't know how to reach that answer.

Thanks in advance.

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- Jun 2nd 2009, 02:09 PMdvh9Triangle help?
Word problem:

The sides of a triangle have lengths x, x+4, and 20. Specify those values of x for which the triangle is acute with longest side 20.

The answer is 12 < x <= 16. However, I don't know how to reach that answer.

Thanks in advance. - Jun 2nd 2009, 09:03 PMmlemilys
the triangle inequality states a+b>c

the sum of the 2 shorter sides must be greater than the 3rd longest

(if their sum is shorter you wouldn't be able to create a triangle, if their sum is equal you would just have a line)

consider that in an acute triangle all angles are less than 90 degrees