A triangle has one side length of 12 inches and another of 8 inches. Describe all possible lengths of the third side. Show and explain your reasoning

Answer 1

For any triangle, the sum of any two sides must be greater than the third side. Let's say we have triangle ABC, where a = 12 and b = 8.

a + b > c (1)

a + c > b (2)

b + c > a (3)

From (1);

12 + 8 > c

c < 20

From (2):

12 + c > 8

c > 4

From (3):

8 + c > 12

c > 4

So the possible lengths of c are: 4 < c < 20. Hope this helps!