Apply the triangle inequality THEOREM, to find the range of measures for the third side of a triangle with the first two sides equal to 24 and 30

Answer 1

According to the triangle inequality theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let the third side be x.

So, applying the triangle inequality theorem:

30 + 24 > x
54 > x

Also,
24 + x > 30
x > 6

Therefore, the range of measures for the third side of the triangle is 6 < x < 54.