In ΔABC, D and E are points on AB and AC respectively. If AB = 33, AC = 21, BC = M, and AD = DE = EC = N, where M and N are integers, find the value of M.

Question

asked May 6, 2024 141k views

1 Answer

Mina Mikhael · Answer 1 · 2024-05-10T19:40:51+0000

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.

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.