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

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, \(3x + 7x>h\) and \(3x+h > 7x\) and \(7x + h>3x\). The third inequality \(7x + h>3x\) is always true for non - negative values of \(x\) and \(h\).
From \(3x + 7x>h\), we get \(h<10x\).
From \(3x+h > 7x\), we get \(h>7x - 3x\), so \(h > 4x\).

Answer:

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