SOLUTION: Trapezoid ABCD has parallel sides AB and CD, of lengths 8 and 16, respectively. Diagonals AC and BD in- tersect at E, and the length of AC is 15. Find the lengths of AE and EC.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Trapezoid ABCD has parallel sides AB and CD, of lengths 8 and 16, respectively. Diagonals AC and BD in- tersect at E, and the length of AC is 15. Find the lengths of AE and EC.      Log On

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Question 1157984: Trapezoid ABCD has parallel sides AB and CD, of
lengths 8 and 16, respectively. Diagonals AC and BD in- tersect at E, and the length of AC is 15. Find the lengths of AE and EC.
Answer by ikleyn(52781) About Me  (Show Source):
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Notice that the triangles AEB and CED are similar, with the similarity coefficient  |AB| : |CD| = 16:8 = 2 (from greater to smaller).


Therefore, the segments AE and EC are in proportion 2, too.


Since their total length is  |AC| = 15, the segments  AE and EC are 10  and 5 units long.

Solved.