Question

∆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 : 17

This 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 1

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

\(\frac {area \, of \, \triangle ABC}{area \, of \, \triangle PQR}=\frac {2.25}{5.29}=\frac {225}{529}\)