Question

The ABC Toy Company is creating two similar pieces for board game, as shown below. Find the value of y that makes the two pieces similar.

Answer 1

A shape that is similar to another shape will be enlarged by a scale factor. 
Each corresponding sides should give the same scale factor

Side GI corresponds to side JL
Side GH corresponds to side JK
Side HI corresponds to side KL

The correspond sides whose length are given is 
GH = 4 and JK = 8

Side JK is twice longer than GH

All the other sides of triangle JKL are twice longer than triangle GHI, so we want that the side JL to be twice of the sides GI

Side GI = 6
Side JL = 6 × 2 = 12

Answer: y = 12