Answer:
A. 9 inches.
Step-by-step explanation:
Let x represent the 3rd side of the triangle.
We have been given that the lengths of two sides of a triangle are 12 inches and 4 inches. We are asked to find the possible dimension of the third side of the triangle.
We will use triangle inequality theorem to solve the given problem. Triangle inequality theorem states that the one side of a triangle must be smaller than the sum of other two sides of the triangle.
Using triangle inequality theorem we can set two inequalities as:
[tex]x+4>12[/tex] and [tex]x<4+12[/tex]
[tex]x+4-4>12-4[/tex] and [tex]x<16[/tex]
[tex]x>8[/tex] and [tex]x<16[/tex]
Upon combining both inequalities we will get,
[tex]8<x<16[/tex]
This means that the measure of third side of the triangle can be any length greater than 8 and less than 16.
Upon looking at our given choices, we can see that option A is the correct choice.
