The lengths of the sides, , of ΔABC are in the ratio 3 : 4 : 5. Correspondence ABC ↔ PQR is similarity. If PR = 12, the perimeter of ΔPQR is ……….

Given: In ∆ABC,

BC:CA:AB = 3:4:5

From ∆ABC and ∆PQR, the correspondence ABC ↔ PQR is similarity.

In ∆PQR,

PR = 12

To find: Perimeter of ∆PQR = ?

In ∆ABC, since we have BC:CA:AB = 3:4:5

Let the lengths of BC, CA and AB be 3t, 4t and 5t respectively. (where, t > 0)

Perimeter of ∆ABC = 3t + 4t + 5t

⇒ Perimeter of ∆ABC = 12t, t > 0

Also, from given we have,

In ∆ABC and ∆PQR, the correspondence ABC ↔ PQR is similarity.

So, from property we can say that,

Ratio of perimeters of ∆ABC and ∆PQR = Ratio of their corresponding sides

⇒

Substituting the given values, we get

⇒

⇒ Perimeter of ∆PQR = 36

Thus, option (b) is correct.