Question

Find the value of X?

Answer 1

The answer is 4. :)

Explanation:

I am assuming the question is asking for the value, when added to 2, will give you the length of segment BE.

We have a set of similar triangles here. `triangle`BAE is the smaller one, and `triangle`CAD is the larger. We know the triangles are similar due to side-angle-side. `(CA)/(BA) = (DA)/(EA)` and both triangles share `angleA`

Now we can set up a proportion: `(BA)/(BE)=(CA)/(CD)`

When we plug in the values of these sides we get: `(10)/(x+2)=(20)/(12)`

Now comes the algebra: `120 = 20(x+2)`

`120 = 20x +40`

`120-40 = 20x-40`

`80=20x`

`(80)/(20) = (20x)/(20)`

`4=x`