The Sides Of A Triangle Are 8 Cm, 9 Cm And 13 Cm. The Longest Side Of A Similar Triangle Is 19.5 Cm. What Is The Perimeter Of The Similar Triangle?

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)