1) You have vertical angles here. This means the big and small triangles are similar, meaning the ratio of corresponding sides of the two triangles are equal.
In this case, 32cm corresponds to 4cm and 40cm corresponds to x. To find x, set up the ratio as follows: 4/32 = x/40.
4/32 can be reduce to 1/8. Multiply each side by 40 to isolate x. you get 1/8 * 40
This yields x = 5 cm
2) set up a proportion, similar to the first question.
(x + 4)/8 = (2x + 1)/12
12(x + 4) = 8(2x + 1)
12x + 48 = 16x + 8
40 = 4x
x = 10
the length of BC is (x + 4) + (2x + 1) = 3x + 5
this means BC = 35