Question

The lengths of the sides BC, CA, AB of ΔABC are in the ratio 3:4:5. Correspondence ABC ⇔ PQR is similarity. If PR=12, the perimeter of ΔPQR is ......,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 12
(b) 36
(c) 24
(d) 27

Answer 1

Given : in ∆ABC , the lengths of the sides BC, CA, AB of ΔABC are in the ratio 3:4:5.
Let proportionality constant is x
then, BC = 3x, CA = 4x and AB = 5x
so, perimeter of ∆ABC = BC + CA + AB
= 3x + 4x + 5x = 12x ....(i)

also we have given, Correspondence ABC ⇔ PQR is similarity.
but we know, ratio of perimeter of triangles = ratio of their corresponding sides,
e.g., perimeter of ∆ABC/perimeter of ∆PQR = AB/PQ = BC/QR = AC/PR .......(ii)

12x/perimeter of ∆PQR = AC/PR [ from eq. (i)]
12x/perimeter of ∆PQR = 4x/12
perimeter of ∆PQR = 36

hence, option (b) is correct

Answer 2

In the attachment I have answered this problem.

Concept:

If two triangles are similar then their

Corresponding sides are proportional.

See the attachment for detailed solution.