Determine the possible side lengths of the third side of a triangle with known side lengths of 6 and 12. A) 6 < c < 18 B) - 6 < c < - 18 C) 12 < c < 6 D) 6 < c < 12

A) 6 < c < 18

Step-by-step explanation:

A triangle is known to have 3 sides: Side a, Side b and Side c.

For a triangle, one of the three sides is longer than the other two sides. (The only exception is when we are told specifically that a triangle is an equilateral triangle, where all the 3 sides are equal to each other).

To solve the above question, we would be using the Triangle Inequality Theorem.

The Triangle Inequality Theorem states that the summation or addition of the lengths of any two sides of a triangle is greater than the length of the third side.

Side a + Side b > Side c

Side a + Side c > Side b

Side b + Side c > Side a

For the above question, we have 2 possible side lengths for the third side of the triangle. We are given in the above question,

side (a) = 6

side (b) = 12

Let's represent the third side as c

To solve for the above question, we would be having the following Inequality.

= b - a < c < b + a

= 12 - 6 < c < 12 + 6

= 6 < c < 18

Therefore, the possible side lengths for the triangle is the above question is Option A) 6 < c < 18