Can someone help me find the ratio for the sides of this triangle?

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Answer 1 · 2018-02-21T11:49:25

As detailed below.

Given #DE# parallel #AB#

Consider triangles CDE & CAB.

#hat(CDE) = hat(CAB)# ( corresponding angles.

#hat(CED) = hat(CBA)# ( corresponding angles.

#hat C# common.

Hence, two triangles are similar.

#:. (AC) / (DC) = (BC) / (EC) = (AB) / (DE)# Eqn (1)

(6.) but #AC = AD + DC# and #BC = (BE + EC)#

#:. (AD+ DC) / ((DC) = (BE + EC) / (EC)#

#(AD) / (DC) + cancel1 = (BE) / (EC) + cancel1#

#(AD) / (DC) = (BE) / (EC)#

But given #(AD) / (DC) = 1/3#

#:. (EB) / (EC) = 1/3# or #(EC) / (EB) = 3 / 1 = 3#

(7.) Measurements are known for #AB, AD, BC#

Substituting in (1),

#(color(purple )(AD) + DC) / (DC) = color(purple)(BC) / (EC) = color(purple)(AB) / (DE)#

Hence, at least one more side measurement is needed to find the lengths of other sides.