The extensions of the legs ab and cd of a trapezoid abcd intersect at point e. find the lengths of the sides of △aed if ab=5cm, bc=10cm, cd=6cm, ad=15cm.

  AE = 15 cm; ED = 18 cm; AD = 15 cm (given)

Step-by-step explanation:

ΔBEC ~ ΔAED so ...

   AD/BC = AE/BE = (BE+AB)/BE = 1 + AB/BE

Substituting given numbers (lengths in centimeters), we have ...

  15/10 = 1 + 5/BE

  1/2 = 5/BE

  BE = 10

Similarly, ...

  1/2 = 6/CE

  CE = 12

Then the unknown sides are ...

  AE = AB + BE = 5 + 10 = 15 . . . cm

  ED = CE + CD = 12 + 6 = 18 . . . cm

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step-by-step explanation:

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step-by-step explanation: