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.

1 answer

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, let's assume that the third side has a length of x.

According to the Triangle Inequality Theorem, we have the following inequality: 24 + 30 > x

Simplifying the inequality, we get: 54 > x

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