Question

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.

Answer 1

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

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