Question

A triangle has one side that is 5 inches long and another that is 7 inches long. How many different lengths, in inches,are possible for the last side of the triangle?

Answer 1

2 < c < 12

Explanation:

Let the last side of the triangle = c

The sum of any two sides must be greater than the third side. Let's say we have triangle ABC, where a = 5 inches and b = 7 inches

a + b > c (1)

a + c > b (2)

b + c > a (3)

From (1);

a + b > c

7 + 5 > c

c < 12

From (2):

a + c > b

7 + c > 5

7 - 5 < c

c > 2

From (3):

b + c > a

5 + c > 7

c > 7 - 5

c > 2

So the possible lengths of c are: 2 < c < 12