document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105846>Question 1105846</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In triangle ABC ,PQ is parallel to AC and PQ divides triangular region ABC into two parts such that ar(BPQ)=1/4 at(PQCA). Find BP:PA.<BR>\n" );
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document.write( "If the area of triangle BPQ is 1/4 the area of trapezoid PQCA, then the area of triangle BPQ is 1/5 the area of triangle ABC.<br><BR>\n" );
document.write( "Since triangles ABC and PBQ are similar, the ratio of their areas is the square of the scale factor between the two triangles.<br><BR>\n" );
document.write( "Since the ratio of areas is 1:5, the scale factor is 1:sqrt(5); that makes BP:AB = 1:sqrt(5).  And that makes BP:PA = 1:(sqrt(5)-1). </SPAN>\n" );
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