The sides of an integral triangle are 4,8 and (20-2x).

Question

The sides of an integral triangle are 4,8 and (20-2x). Find the sum of all values of x?

Answer 1

4+8 > 20-2x any side of a triangle is less than the sum of the other two sides

6 > 10-x

-4 > -x

4 < x

x >4

8-4< 20-2x any side of a triangle is greater than the difference between the other two sides

4 < 20-2x

2 < 10-x

-8 < -x

8 > x

x < 8

4 < x < 8

x = integer, so x = 5, 6 or 7

sum = 18