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.

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10