Question

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?

Answer 1

The answer is 4x cm < h < 10x cm.

The third side of the triangle is greater than the difference of the lengths of the other two sides (h > 7x cm - 3x cm) and it is less than the sum of the lengths of the other two sides (h < 7x cm + 3x cm). Therefore:
h > 7x - 3x
h < 7x + 3x

This can be expressed as:
7x cm - 3x cm < h < 7x cm + 3x cm
⇒ 4x cm < h < 10x cm