Find the value of X?

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1 Answer
Mr. Math
May 16, 2018

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#

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