Question

What will be the ratios of areas of similar ∆ABC and ∆PQR, if the altitudes of the triangles are 10cm and 5.5cm respectively?

(a) 150 : 4

(b) 300 : 7

(c) 100 : 3

(d) 400 : 9

The question was asked during an online exam.

The query is from Area of Similar Triangle topic in chapter Triangles of Mathematics – Class 10

Answer 1

The correct answer is (d) 400 : 9

For explanation I would say: We know that the ratio of areas of similar triangles is equal to the ratio of the squares of their corresponding altitudes.

Here, AD = 10cm and PS = 5.5 cm

According to the theorem,

\(\frac {area \, of \, \triangle ABC}{area \, of \, \triangle PQR}=(\frac {AD}{PS})\)^2

\(\frac {area \, of \, \triangle ABC}{area \, of \, \triangle PQR}=(\frac {10}{5.5})\)^2

\(\frac {area \, of \, \triangle ABC}{area \, of \, \triangle PQR}=\frac {100}{2.25}=\frac {400}{9}\)