What is be ? i am posting a lot of these questions to understand shapes better, i want explained answers

Find the scale factor of the two triangles by dividing the lengths of the two given sides that are the same orientation:  

From this picture the smaller triangle is mirrored across the X and Y axis so AD and EC are the same leg

AD= 12 and EC = 3

 The scale factor is 12/3 = 4, this means that DB is 4 times larger than BE

So we can set up an equation and solve:

k+5 = 4(k-7)

Distribute the right side:

k+5 = 4k-28

subtract 1 k from each side:

5 = 3k -28

add 28 to each side:

33 = 3k

Divide both sides by 3:
k = 33/3
k = 11

Now we know the value for k we can calculate BE by replacing k with 11:

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

The length of BE is 4

Hi,

Using Thales 's theorem,

Wow. that is a really cool question.