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mathwizzard3
So first of all the triangle is flipped so the corresponding sides are a little confusing to see. Either way HJ and DF correspond meaning 9 and 12 correspond.

What's the relation? Well 9/12 is 3/4 so each side of the small one is 3/4 of the big one!

GH and CD correspond so 12 is 3/4 of CD

So set up this equation:

12 = 3/4*CD
Multiply by 4/3
16=CD

That's your answer for the first one^

Now finding the perimeter is just adding all the sides so we have two of the sides, 16 and 12 but we need to find the hypotenuse. We can do the same thing earlier just with the hypotenuse side!
15 = 3/4*FC
4/3 times both sides
20=FC

So just add 20 and 16 and 12 which is 48! 48 is your perimeter! 

Hope that helps! :3

- mathwizzard3


Doyalikedagz
Alrighty, so, here's what's up:
Part A: 
Write a proportion that can be used to find the length of side CD.
How I would do it:
You're given one side on the large triangle which measures 12.
The corresponding side on the smaller triangle measures 9.
Your proportion would be 9/12, this simplifies to 3/4.
This means that x (Side CD), when multiplied by 3/4 equals 12.
x*(3/4)=12
x=16
Part B:
What is the perimeter in units of triangle CDF?
The perimeter of a triangle is a+b+c, where a, b, and c are the sides of the triangle. We have sides a, and b already. a=12, b=16. Now we just need to find side c. You can find side c by using
the 3/4 proportion.
x*(3/4)=15
x=20
Side c=20
Now add up all of the sides: 12+16+20=48
The perimeter of the triangle is 48 units.

Hope this helps! (: