If $14.8:x::x:3.7$ and $x>0$, then find the value of x.

The correct option is 7.4.

To find the value of $x$, we start with the given proportion:

$14.8:x::x:3.7$

A proportion of the form $a:b::c:d$ can be rewritten as an equation of ratios:

$\frac{14.8}{x}=\frac{x}{3.7}$

By cross-multiplying the terms, we get:

$x^2=14.8\times 3.7$

Now, let's calculate the product on the right side of the equation. We can rewrite the decimals as fractions to make the multiplication easier:

$14.8=\frac{148}{10}$
$3.7=\frac{37}{10}$

Substitute these back into the equation:

$x^2=\frac{148}{10}\times \frac{37}{10}$

Notice that $148=4\times 37$. We can write:

$x^2=\frac{4\times 37\times 37}{100}$

$x^2=\frac{4\times {37}^2}{100}$

Taking the square root on both sides, and using the condition that $x>0$:

$x=\sqrt{\frac{4\times {37}^2}{100}}$

$x=\frac{2\times 37}{10}$

$x=\frac{74}{10}$

$x=7.4$

Thus, the value of $x$ is indeed $7.4$.