The two triangles are similar. There are two possible values of x. Work out each of these values. State both assumptions you make in your working. You must state which two triangles you are assuming to be similar.

Step-by-step explanation:

ΔABE ~ ΔACD

  AC/AB = AD/AE

  (10+x)/10 = (15+3)/15

  1 +x/10 = 1 +0.2 . . . expand each ratio

  x = 10(0.2) . . . . . . . subtract 1 and multiply by 10

  x = 2

__

ΔABE ~ ΔADC

  AC/AE = AD/AB

  (10+x)/15 = (15+3)/10

  10 +x = 27 . . . . . . . . multiply by 15

  x = 17 . . . . . . . . . . . . subtract 10

Additional comment

The triangles can be declared similar in 6 ways, but it does no good to match a marked side with an unmarked side. Hence, only two of the possible similarity statements will result in a solution for x.

a line

Step-by-step explanation:

Here is ray AB  

     A                         B

     ++>

It starts at point A, goes through point B, and goes only in one direction, to the right. Points A and B lie on line AB.

Now I'll add an opposite ray whose endpoint is also point A.

             C                A                         B

<+++>

Ray AC also lies on the same line as ray AB, but starting at point A, it goes in the opposite direction of ray AB. When you add ray AC to its opposite ray AB, you get the entire line AB.

a line