Question

What is DE? Enter your answer as a decimal in the box. units The figure shows what appears to be acute triangle A B C. Point D is on side A B. Single tick marks pass through segments A D and D B. Point E is on side B C. Double tick marks pass through segments B E and E C. Segment D E is drawn. The length of side C A is 12.6.

Answer 1

6.3

Explanation:

You want the length of midsegment DE, parallel to CA, given as length 12.6.

Midsegment

∆BDE ~ ∆BAC, so ...

BD/BA = DE/AC . . . . . corresponding sides are proportional

BD/(BD +DA) = BD/(BD +BD) = 1/2 = DE/12.6

Multiplying by 12.6, we get ...

DE = 12.6(1/2) = 6.3

The length of DE is half the length of CA, so is 6.3.

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Additional comment

We cannot tell if 6 is supposed to be the answer to the question with ending statement, "The length of side CA is 12." (6 would be the correct answer in that case.) We have assumed that segment CA is 12.6, as written.

The length of a triangle midsegment is always half the length of the parallel base. (A "midsegment" joins the midpoints of the segments it intersects.)