A smaller triangle with side lengths 9 millimeters and 6 millimeters. A larger triangle with side lengths x millimeters and 16 millimeters. Which proportional statements are true for finding the value of x? Check all that apply.
StartFraction 6 over x EndFraction = StartFraction 9 over 16 EndFraction
StartFraction 6 over 16 EndFraction = StartFraction 9 over x EndFraction
StartFraction 9 over 6 EndFraction = StartFraction x over 16 EndFraction
StartFraction 9 over x EndFraction = StartFraction 16 over 6 EndFraction
StartFraction 9 over x EndFraction = StartFraction 6 over 16 EndFraction

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.

step-by-step explanation:

it's is b

the 4th choice is the correct one

step-by-step explanation: