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 inches

Question

and a second side that is 4 inches less than twice the third side, what are the possible lengths for the second and third sides?

Answer 1

Let x = the length of the 3rd side

Let 2x - 4 = the length of the 2nd side

x + 2x - 4 > 8

3x > 12

x > 4, 3rd side 

 

If 3rd side = 5, the second side = 2(5) - 4 = 6

If 3rd side = 6, the second side = 2(6) - 4 = 8

If 3rd side = 7, the second side = 2(7) - 4 = 10

If 3rd side = 8, the second side = 2(8) - 4 = 12

If 3rd side = 9, the second side = 2(9) - 4 = 14

If 3rd side = 10, the second side = 2(10) - 4 = 16

If 3rd side = 11, the second side = 2(11) - 4 = 18

If 3rd side = 12, the second side = 2(12) - 4 = 20 - this one doesn't work because your sides are 8, 12, and 20. 8 + 12 is not greater than 20.

 

This does not consider sides that could be fractions, like 8 1/2.