Question

A triangle has two sides of length 1 and 2. What compound inequality describes the possible lengths for the third side, x?Write a compound inequality like 1

Answer 1

Explanation:

since in a triangle each side must be shorter than the sum of the other 2 sides (otherwise the end points cannot connect, and there is no triangle), the necessary inequality condition must be

side < 1 + 2 = 3

so,

side < 3

for a lower limit let's go through the cases

1 < 2 + side (is always true)

2 < 1 + side

1 < side (side must be larger than 1)

and again

side < 1 + 2 = 3

side < 3

so the full restriction for the third side is

1 < side < 3