SOLUTION: We are learning about similar triangles (AA, SSS & SAS) and I am stuck on the following problem: If EF || AB, AD=9, DB=16, EC=2(AE), find AE, AC, CF, CB, CD, and EF. (the book s

Question 410380: We are learning about similar triangles (AA, SSS & SAS) and
I am stuck on the following problem:
If EF || AB, AD=9, DB=16, EC=2(AE), find AE, AC, CF, CB, CD, and EF.
(the book says the answers are: 5, 15, 13.3, 20, 12 and 16.6 - but I am not sure how)
Can someone help?
Thanks.

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
CEF is similar to CAB (CAB is obviously larger)

EC = 2(AE) so EC is 2/3 of AC ___ the ratio between corresponding similar sides is 2:3

angle C is a right angle (the triangles are right triangles)

so using the ratio (2:3) , the given lengths , and the Pythagorean theorem (a^2 + b^2 = c^2) ;
you can find all the missing lengths

HINT : because EF║AB and CD┴AB , ALL the triangles are similar
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