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.

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(52780) (Show Source): You can put this solution on YOUR website!
.


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.

RELATED QUESTIONS
.Trapezoid ABCD has parallel sides AB and CD, of lengths 12 and 18, respectively.... (answered by greenestamps)

890.Trapezoid ABCD has parallel sides AB and CD, of lengths a and b respectively.... (answered by AnlytcPhil,Edwin McCravy)

In trapezoid ABCD segments AB and CD are parallel. Point P is the intersection of... (answered by math_tutor2020)

Trapezoid ABCD has parallel sides AB and CD, a right angle at D, and the lengths AB = 15. (answered by orca)

given trapezoid abcd with diagonals ac and bd intercept at point e prove triangle dec is... (answered by solver91311)

In rectangle ABCD, diagonals AC and BD intersect at Point E. If AC=36 and BD=2x+30, find... (answered by math-vortex)

In trapezoid ABCD, diagonals AC,BD intersect at M. AD is parallel to BC and MN. AD=3,... (answered by ikleyn)

In a trapezoid ABCD with legs AB and CD, the diagonals intersect each other at point O. (answered by MathLover1)

An isosceles trapezoid ABCD, AB = 5, BC & AD = 3 and CD = 8. Find the length of the... (answered by ikleyn)