∆ABC ∼ ∆PQR, AD & PS are the angle bisectors of respectively. If AD = 1.5cm and PS = 2.3 cm then, what will be the ratio of the areas of ∆ABC and ∆PQR?(a) 19 : 15(b) 225 : 529(c) 529 : 225(d) 15 : 17This question was posed to me in an interview for internship.My question is from Area of Similar Triangle topic in portion Triangles of Mathematics – Class 10

∆ABC ∼ ∆PQR, AD & PS are the angle bisectors of respectively. If

1.	∆ABC ∼ ∆PQR, AD & PS are the angle bisectors of respectively. If AD = 1.5cm and PS = 2.3 cm then, what will be the ratio of the areas of ∆ABC and ∆PQR?(a) 19 : 15(b) 225 : 529(c) 529 : 225(d) 15 : 17This question was posed to me in an interview for internship.My question is from Area of Similar Triangle topic in portion Triangles of Mathematics – Class 10
Answer» Correct answer is (b) 225 : 529 The BEST explanation: We know that the RATIO of AREAS of similar triangles is equal to the ratio of the squares of their CORRESPONDING angle bisectors. Here, AD=1.5 cm and PS=2.3 cm According to the THEOREM, \(\frac {area \, of \, \triangle ABC}{area \, of \, \triangle PQR}=(\frac {AD}{PS})\)^2 \(\frac {area \, of \, triangle \, ABC}{area \, of \, triangle \, PQR}=(\frac {1.5}{2.3})\)^2 \(\frac {area \, of \, \triangle ABC}{area \, of \, \triangle PQR}=\frac {2.25}{5.29}=\frac {225}{529}\)

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