Answer:
Step-by-step explanation:
First of all, write the similarity statement for the triangles.
ΔCDE ~ ΔCBA
Identify the line segments in each triangle that you know. Preferably, choose ones that correspond.
CE = 27, DE = the length we want to find . . . . known segments in ΔCDE
CA = (18+27) = 45 . . . . . corresponds to CE
BA = 28 . . . . . . . . . . . . . corresponds to DE
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The ratios of corresponding line segments are equal:
DE/CE = BA/CA . . . . this is the proportion you want to set up*
DE/27 = 28/45
Multiply by the denominator of DE/27 to eliminate that:
DE = 27(28/45)
DE = 16.8
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* I usually choose to put the unknown variable in the numerator of a proportion, so that solving it only involves multiplication by the denominator. If you put the variable in the denominator, the solution takes an extra step.
