Question

Two triangles are similar. The ratio of their corresponding sides
1:4.

1. Find the ratio of their perimeters

2. What is the ratio of their areas

Answer 1

each side of the big one is 4 times the one in the small triangle
4a+4b+4c = 4(a+b+c)

the altitude of the big one is 4 timess the altitude of the small one
(1/2)(4h)(4b) = (16) (1/2) a b

Answer 2

The ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.

In this case

P1 : P2 = 1 : 4

The ratio of the area of two similar triangles is proportional to square of the ratio of their corresponding sides.

In this case

A1 : A2 = ( 1 : 4 )² = 1 / 16