Question

The sum of the lengths of any two sides of a triangle must be greater than the third side. if a triangle has one side that is 8 cm and a second side that is 1 cm less than twice the third side, what are the possible lengths for the second and third sides?

Answer 1

1st Side: 8

2nd Side: 2x - 1

3rd Side: x

(8) + (2x - 1) > x            (2x - 1) + x > 8                        (x) + (8) > 2x - 1

       2x + 7 > x                     3x - 1 > 8                                8  > x - 1

            2x > -7                         3x > 9                                9  > x

             x > -3.5 (disregard)       x > 3                                 x < 9

3rd Side: x  ⇒ (3 < x < 9)

2nd Side: 2x - 1 ⇒ 2(3) - 1 < x < 2(9) - 1   ⇒   5 < x < 17

Answer: the 3rd side must be between 3 and 9, the 2nd side must be between 5 and 17