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Harman [31]
3 years ago
14

The two triangles are similar. There are two possible values of x. Work out each of these values. State both assumptions you mak

e in your working. You must state which two triangles you are assuming to be similar.

Mathematics
1 answer:
Anit [1.1K]3 years ago
4 0

Answer:

  • ΔABE ~ ΔACD, x = 2
  • ΔABE ~ ΔADC, x = 17

Step-by-step explanation:

<u>ΔABE ~ ΔACD</u>

  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

__

<u>ΔABE ~ ΔADC</u>

  AC/AE = AD/AB

  (10+x)/15 = (15+3)/10

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

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

_____

<em>Additional comment</em>

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.

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