Final answer:
In ΔABC, if AD = DE = EC, and AB = 33 and AC = 21, we can use the triangle inequality theorem to find the value of BC.
Step-by-step explanation:
Let's start by drawing the diagram of ΔABC:
AB is the side opposite to ∠C, AC is the side opposite to ∠B, and BC is the side opposite to ∠A.
We are given that AD = DE = EC = N. This means that the lengths of segments AD, DE, and EC are all equal to N.
Since AD+DE+EC = AC, we can write N + N + N = 21. Simplifying this equation gives 3N = 21. Dividing both sides by 3, we find N = 7.
Now, we know that AB = 33, AC = 21, and AD = DE = EC = 7.
Using the triangle inequality theorem, we can determine that BC = AB - AC = 33 - 21 = 12.
Therefore, the value of M is 12.
Learn more about Triangle Inequality Theorem