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 - side - length relationship

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side, and the difference between the lengths of any two sides must be less than the length of the third side.
Let \(a = 3x\), \(b=7x\). Then \(b - a\lt h\lt a + b\).

Step2: Calculate \(b - a\) and \(a + b\)

Calculate \(b - a\): \(7x-3x = 4x\).
Calculate \(a + b\): \(3x + 7x=10x\).

Answer:

\(4x\lt h\lt10x\) (the first option)