Question

The perimeters of two similar triangles ABC, PQR is 64 cm and 24 cm respectively. If PQ is 12 cm what will be the length of AB?

(a) 30 cm

(b) 32 cm

(c) 12 cm

(d) 16 cm

This question was addressed to me in class test.

This key question is from Criteria for Similarity of Triangle topic in portion Triangles of Mathematics – Class 10

Answer 1

Correct option is (b) 32 cm

For explanation: We know that the ratio of the perimeters of similar triangles is the same as the ratio of their corresponding sides.

∴ \(\frac {Perimeter \, of \, \triangle ABC}{Perimeter \, of \, \triangle PQR} = \frac {AB}{PQ}\)

\(\frac {64}{24}=\frac {AB}{12}\)

AB = \(\frac {64\times 12}{24}\) = 32 cm