In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation. > Solution The correct option is B False The sum of the length of any two sides of a triangle is always greater than the third side. Hence, the given statement is false. a+b>c a+c>b b+c>a
10 Hannah B. the sum of the lengths of any 2 sides of a triangle must be greater than the third side. one side is 17cm and second side is 1 cm less than twice the third side. what are the possible lengths for the second and third sides? 1 Expert Answer
Jordan K. answered • 10/20/15 Nationally Certified Math Teacher (grades 6 through 12)
Let's begin by identifying the lengths of the three sides of the triangle: length of side 2 = 2x - 1 (1 less than twice side 3) Now let's apply the Triangle Inequality Theorem to this triangle: side 1 + side 2 > side 3: x > -16 (reject negative measurement) 2x - 1 > -33 (reject negative measurement) Thus, we have our answers based on the value of x: 6 < x (length of side 3) < 18 11 < 2x - 1 (length of side 2) < 35 Thanks for submitting this problem and glad to help. |