The problem states that the mean proportional between $x$ and $272$ is $68$. We need to find the value of $x$.

1. Problem Description

The problem states that the mean proportional between $x$ and $272$ is $68$. We need to find the value of $x$.

2. Solution Steps

The mean proportional between two numbers $a$ and $b$ is $\sqrt{ab}$.

Given that the mean proportional between $x$ and $272$ is $68$, we can write the equation:

$\sqrt{x \cdot 272} = 68$

Squaring both sides of the equation, we get:

$x \cdot 272 = 68^2$

$x \cdot 272 = 4624$

Divide both sides by 272:

$x = \frac{4624}{272}$

$x = 17$

3. Final Answer

The value of $x$ is 17.