Geometry Problem

Click the figure below to see the complete problem 470 about Triangle, Parallel, Parallelogram, Area, Similarity.

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Complete Problem 470

Level: High School, SAT Prep, College geometry

## Saturday, July 10, 2010

### Problem 470: Triangle, Parallel, Parallelogram, Area, Similarity

Labels:
area,
parallel,
parallelogram,
similarity,
triangle

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Triangles BDE, EFC & BAC are similar and hence, S1/S = BE^2/BC^2, S2/S=EC^2/BC^2 or √(S1/S)=BE/BC & √(S2/S)=EC/BC and hence √(S1/S)+√(S2/S)= BE/BC + EC/BC=BC/BC=1 or √S=√(S1 + √(S2 ---(1) Now square both sides of this to obtain, S =S1+S2+2√(S1S2)or S-S1-S2=2√(S1S2)or S3=2√(S1S2)---(2)

ReplyDeleteVihaan