Answer:
10 cm
Simplified explanation/tl;dr: the small triangle is two thirds the size of the big triangle, so the missing side on the small triangle is two thirds the size of the same side on the big triangle
Long explanation/step by step:
It looks scary, but don't worry; for questions like this just find the ratio then multiply it by the similar side to find the missing side.
This is what I mean: 8/12 simplified is 2/3 (4 is the common factor and 8/4 = 2 and 12/4 = 3). That's your fraction to multiply by.
I chose 8 and 12 because look how the triangles are the same shape just different sizes, that means they're similar. the similar sides are just the same side on both triangles. (for this one, BC and GH are similar). to find how much smaller it is in fraction form, you just take two of the same sides and divide the small one by the big one. (big number becomes top, small becomes bottom)
now just multiply 15 by 2/3 by using fraction multiplication. 15/1 x 2/3 = 30/3. Simplify that to 10/1 (3 is the common factor and 30/3 = 10 and 3/3 = 1). 10/1 = 10.
