Question

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side

7,10

Answer 1

The third side must be greater than 3, otherwise it couldn't reach
the ends of the 7 and 10.

Also, it must be less than 17, otherwise the 7 and 10 couldn't reach
the ends of it.

Answer 2

the triangle inequality theorem states that any side of a triangle is always shorter than the sum of the two other sides.

so if the two other sides are 7 and 10, the sum of the two other sides is 17 (7+10=17)

therefore, the third side must be shorter than 17