Question

given a triangle with side lengths 5 and 8 find the range of the possible values for the third side, x.

Answer 1

If a triangle has the lengths of 3 sides a, b, and c

Then the length of any side must lie between the different and the sum of the other two sides

a - b < c < a + b

a - c < b < a + c

b - c < a < b + c

Let us use this rule to solve the question

Since the triangle has 2 sides 5 and 8

Since 8 - 5 = 3, and 8 + 5 = 13, then

The third side must lie between 3 and 13

3 < 3rd side < 13