SOLUTION: The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has a side that is 20 cm and a second that is 4 cm less than twice the thir

Question 1110384: The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has a side that is 20 cm and a second that is 4 cm less than twice the third side, what are the possible lengths for the second and third side?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The side lengths are 20, x, and 2x-4.

(1) If 20 is the long side, then

x has to be greater than 8.

To verify that this is a limiting value, note that if x=8 the sides are 20, 8, and 12, and the sum of the two short side lengths is exactly equal to the long side.

(2) If 2x-4 is the long side, then

>br>
x has to be less than 24.

Again letting x be 24 we get side lengths of 20, 24, and 44; and again the sum of the two short side lengths is exactly equal to the long side.

Answer: x can be any number greater than 8 and less than 24.
RELATED QUESTIONS
The sum of the lengths of any two sides of a triangle must be greater than the third... (answered by ankor@dixie-net.com)

The sum of the lengths of any two sides of a triangle must be greater than the third... (answered by Edwin McCravy)

The sum of the lengths of any two sides of a triangle must be greater than the third... (answered by sudhanshu_kmr)

The sum of the lengths of any two sides of a triangle must be greater than the third... (answered by josgarithmetic)

The sum of the lengths of any two sides of a triangle must be greater than the third... (answered by robertb)

The sum of the lengths of any two sides of a triangle must be greater than the third... (answered by Boreal,MathTherapy,ikleyn)

The sum of the lengths of any two sides of a triangle must be greater than the... (answered by Alan3354)

The sum of the lengths of any two sides of a triangle must be greater than the third... (answered by stanbon,MathTherapy)

The sum of the lengths of any two sides of a triangle must be greater than the third... (answered by rapture,ikleyn)