We can use the sides of the smaller triangle as ratios:

Sides of smaller triangle:

a : B : C

8 : 9 : 13

The longest side here is 13 cm.

If the largest side of the similar triangle is 19.5 cm, we can say that:

13x = 19.5

x = 19.5/13

x = 1.5

Thus the other sides of the triangle are:

a x 1.5

= 8 x 1.5

= 12 cm

b x 1.5

= 9 x 1.5

= 13.5 cm

Thus the sides of the similar triangle are:

12, 13.5 and 19.5 cm

Therefore, its perimeter would be:

12 + 13.5 + 19.5

= 45 cm (ANSWER)

Sides of smaller triangle:

a : B : C

8 : 9 : 13

The longest side here is 13 cm.

If the largest side of the similar triangle is 19.5 cm, we can say that:

13x = 19.5

x = 19.5/13

x = 1.5

Thus the other sides of the triangle are:

a x 1.5

= 8 x 1.5

= 12 cm

b x 1.5

= 9 x 1.5

= 13.5 cm

Thus the sides of the similar triangle are:

12, 13.5 and 19.5 cm

Therefore, its perimeter would be:

12 + 13.5 + 19.5

= 45 cm (ANSWER)