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Triangle PQR has a right angle at Q and a perimeter of 60. [#permalink]
30 Mar 2008, 11:54
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Triangle PQR has a right angle at Q and a perimeter of 60. Line segment QS is perpendicular to PR and has a length of 12. PQ > QR. What is the ratio of the area of triangle PQS to the area of triangle RQS?
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D. 1-method) Euclid theorem:h^2=m*n=144 m+n=c(hypothenus), where m>n. PQS/RQS=(m/n)^2
only 16 and 9 gives 144 (where m=16x and 9x)
2-method) PQ=a, QR=b and PR=c (hypothenus) a+b+c=60 so a+b=60-c ab/2=12c/2 (triangle area formula) a^2+b^2=c^2 (a+b)^2=a^2+b^2+2ab so (60-c)^2=c^2+24c this gives c=25 now Euclid theorem: 12^2=x(25-x) x=16 or 9 so D.