SOLUTION: If the longest side of a triangle is 10 centimeters, does the perimeter have to be bigger than 20 centimeters? I think the triangle perimeter has to be bigger than 20 centimeters

Question 379565: If the longest side of a triangle is 10 centimeters, does the perimeter have to be bigger than 20 centimeters? I think the triangle perimeter has to be bigger than 20 centimeters because each side would be 10 centimeters and the perimeter would be 30. But my mom says it is possible for a triangle could be equal to 20 centimeters if two sides equal 5 centimeters and the longest side is 10 centimeters. Which is correct? Thank you!
Found 2 solutions by richard1234, mananth:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
If a, b, c are the sides of a triangle and c=10 is the longest side, then by the triangle inequality, a + b > 10. This leaves a + b + c = a + b + 10 > 20, so the perimeter is greater than 20.
A triangle with lengths 5, 5, 10 would be a degenerate triangle.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
If the longest side of the three sides is less than the sum of the other two sides, then a triangle could be formed.
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you should have sum of other two side greater than 10 then a triangle can be drawn.
sum of the other two sides must be >10.
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It is not necessary that the triangle perimeter be more than 30 cm
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