Geometry Problem
Click the figure below to see the complete problem 473 about Triangle, Parallel, Side, Parallelogram, Area, Similarity.
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Complete Problem 473
Level: High School, SAT Prep, College geometry
Thursday, July 15, 2010
Problem 473: Triangle, Parallel, Side, Parallelogram, Area, Similarity
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From P & N draw lines parallel to BC & AC resply. meeting AC in R & T. Hence PN=RG=HT and Tr. DFN/Tr.ABC =(DN/AC)^2 =((DP+PN)/AC)^2 =((AH+HT)/AC)^2 or √(S1/S) = (AH+HT)/AC. Similarly,√(S2/S) = (HT+GC)/AC and √(S3/S)=HG/AC.
ReplyDeleteNow (√S1+√S2+√S3)/√S =(AH+HT+HT+GC+HG)/AC =[(AH+HG+GC)+2HT]/AC=AC/AC+2PN/AC=1+2√(S4/S) which yields the required √S=√S1+√S2+√S3-2√(S4)
Vihaan