Question

a triangle has side lengths measuring 3x cm, 7x cm, and h cm. which expression describes the possible values of h, in cm? 4x < h < 10x 10x < h < 4x h = 4x h = 10x

Explanation:

Step1: Apply triangle - inequality theorem (sum of two sides)

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, \(3x + 7x>h\), which simplifies to \(h < 10x\).

Step2: Apply triangle - inequality theorem (difference of two sides)

The length of any side of a triangle must be greater than the difference between the lengths of the other two sides. So, \(|3x - 7x|0\)), we have \(4x < h\).

Answer:

A. \(4x < h < 10x\)