Q. 7 F5.0( 1 Vote )

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 ……….
A. 12

B. 36

C. 24

D. 27

Answer :

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.

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