document.write( "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! \n" ); document.write( "
Algebra.Com's Answer #269496 by richard1234(7193)![]() ![]() 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.\r \n" ); document.write( "\n" ); document.write( "A triangle with lengths 5, 5, 10 would be a degenerate triangle. \n" ); document.write( " |