Note how all three equations cross multiply to get 6x = 144
==========================================================
Explanation:
One proportion is 9/6 = x/16
Note how the left side is where I'm dividing the sides 9 and 6, which come from the first triangle. The right side x/16 is the same idea, and we're dividing in the same order.
Let's solve for x
9/6 = x/16
9*16 = 6*x
144 = 6x .... cross multiply
6x = 144
x = 144/6
x = 24
If we plugged this into the first answer choice, then we would get
6/x = 9/16
6/24 = 9/16
0.25 = 0.5625
which is a false statement, so choice A is not one of the answers.
Another way we can see that choice A is not an answer is to note that 6/x = 9/16 cross multiplies to 9x = 96, which leads to a different x solution.
-------------
Choice B is one of the answers because 6/16 = 9/x cross multiplies to 6x = 144, which was one of the steps listed above. Therefore 6/16 = 9/x is equivalent to 9/6 = x/16
Choice C is a very similar story. The proportion 9/6 = x/16 is equivalent to 6x = 144 when you cross multiply. So choice C is another answer.
Choice D is not an answer because 9/x = 16/6 cross multiplies to 16x = 54, and we won't get x = 24 if we solved for x.
Choice E is an answer for similar reasoning as choices B and C. The proportion 9/x = 6/16 turns into 6x = 144.
-------------
As a check, you can plug x = 24 into choices B, C and E, and you should get true statements when you simplify.
