If 42 is the mean proportion between x and 294, what is the value of x?

We are asked: 42 is the mean proportion between $x$ and 294. Find $x$.

Step 1: Recall the formula for mean proportion

If m is the mean proportion between $a$ and $b$, then:

$m^2 = a \cdot b$

Here, $m = 42$, $b = 294$, $a = x$

So: $42^2 = x \cdot 294$

Step 2: Solve for $x$

$42^2 = 1764$

So $x \cdot 294 = 1764$ → $x = 1764 / 294 = 6$

✅ Answer: 6