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, \(h<3x + 7x\) and \(3x+h>7x\) and \(7x + h>3x\) (the last one is always true for non - negative side lengths).
From \(h<3x + 7x\), we get \(h<10x\). From \(3x+h>7x\), we can solve for \(h\): \(h>7x - 3x\), so \(h>4x\).

Answer:

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