State which of the following are in proportions.
(iv) $9 : 12 : : 12 : 16$

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Solution

Checking the proportionality:
If four numbers $x, y, z, w$ are in proportion i.e. $x : y : : z : w$ , then the product of extremes is equal to the product of means i.e. $x w = y z$ .
In the given expression, $x = 9, y = 12, z = 12, w = 16$
Now, $x w = 9 \times 16$ $= 144$ and $y z = 12 \times 12$ $= 144$
Therefore, it can be concluded that $x w = y z$
Final Answer: Hence, the given expression represents a proportion.

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