Question

What is BE ? Please explain it in full dont just give me an answer

Answer 1

There are two methods to solve this problem. One of them is the typical method and the other one is the short-cut. I will explain the shortcut

Short-cut: 
This method is quick and easy, and works with ALL triangles, which is why I suggest you use this. You make proportions. Since the triangles are similar, we can use CPCTC. Thereafter,
$\frac{AD}{CE}= \frac{DB}{EB}$

Now, you just need to identify the terms, substitute, and solve for the unknown, which would be k. 

$\frac{12}{3} = \frac{k+5}{k-7} \\ 12(k-7)=3(k+5) \\ 12k-84=3k+15 \\ 9k=84+15 \\ 9k=99 \\ k=11$[/tex]

So we found k, but it is asking for BE. Therefore, plug in the value of k, which is 11, into the expression for BE, which is k-7.

BE=K-7
k=11
BE=11-7
BE=4

Your answer is 4.