Answer:A
Explanation:
To determine the possible values of h, we can apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have side lengths measuring 3x cm, 7x cm, and h cm. Therefore, the possible values of h must satisfy the following conditions:
h + 3x > 7x
h + 7x > 3x
3x + 7x > h
Simplifying these inequalities, we have:
h > 4x
h > -4x (since we have h + 7x > 3x, we can subtract 7x from both sides)
10x > h
From these conditions, we can conclude that h must be greater than 4x and less than 10x. So, the expression that describes the possible values of h is:
h > 4x and h < 10x
Alternatively, we can write it as:
4x < h < 10x
Therefore, the correct option is A) 4x.