Question

A triangle has sides of 5 and 9. What is a possible length of the third side?

Answer 1

Answer:

4 < c < 14

e. g : {5, 6, 7, 8, 9, 10, 11, 12, 13}

Step-by-step explanation:

Let

a, b, c - lengths of sides of a triangle

then:

a + b > c

a + c > b

b + c > a.

We have

a = 5, b = 9

then

c < 5 + 9 → c < 14   (1)

5 + c > 9           subtract 5 from both sides

c > 4   (2)

9 + c > 4             subtract 9 from both sides

c > -5     (3)

From (1), (2) and (3) we have

c < 14 ∧ c > 4 ∧ c > -5 → 4 < c < 14