AB represents the width of a rlver. #\bar(AE)# and #\bar(BD)# intersect at C. #\bar (AB) _|_ \bar (BD)#. and #\bar(ED)# _|_ #\bar (BD)#. If BC = 80 yard, CD = 40 yd, and DE = 2- yard, what is AB?

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Answer 1 · 2018-05-01T04:10:37

#AB = 40#

Given: #bar(AE)# and #bar(BD)# intersect at #C#. #bar(AB)# perpendicular #bar(BD# and #bar(ED)# perpendicular #bar(BD)#. #BC = 80; CD = 40; DE = 2#

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We have two similar triangles, #Delta ABC ~ Delta EDC#

Use proportions to solve for #AB#:

#(AB)/80 = 2/40#

Use the cross-product:

#40 * AB = 2 * 80#

#40 AB = 160#

#AB = 160/40 = 40#