The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. The lengths of two sides of a triangle are 15 ft and 27 ft. Find the possible lengths of the third side.

Question

The third side must have a length greater than
? ft and less than
? ft.

Answer 1

let the third side be x , where x > 0
then x+15 > 27 ---> x > 12
and
x+27> 15 ---> x > -12
so far we have x > 12
and
12+27 > x
x < 39

so :
12 < x < 39