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 2323 cm and a second side that is 44 cm less than twice the third side, what are the possible lengths for the second and third sides?

Answer 1

Let's begin by identifying the lengths of the three sides of the triangle:    length of side 1 = 17    length of side 2 = 2x - 1 (1 less than twice side 3)    length of side 3 = x Now let's apply the Triangle Inequality Theorem to this triangle:    side 1 + side 2 > side 3:        17 + 2x - 1 > x        16 + 2x > x        2x - x > -16        x > -16 (reject negative measurement)        2x - 1 > -33 (reject negative measurement)     side 1 + side 3 > side 2        17 + x > 2x - 1        x - 2x > -1 - 17        -x > -18          x      < 18        2x - 1 < 35    side 2 + side 3 > side 1        2x - 1 + x > 17        3x - 1 > 17        3x > 18          x       >   6        2x - 1 > 11 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