1. The problem is to find the value of $x$ given the lengths 6 cm and 16 cm, but the exact relationship or figure is not specified. 2. Since the problem is unclear, let's assume it might be a right triangle with legs 6 cm and $x$ cm, and hypotenuse 16 cm. 3. Using the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $a=6$, $b=x$, and $c=16$. 4. Substitute the known values: $$6^2 + x^2 = 16^2$$ 5. Calculate squares: $$36 + x^2 = 256$$ 6. Isolate $x^2$: $$x^2 = 256 - 36 = 220$$ 7. Take the square root: $$x = \sqrt{220} = 2\sqrt{55} \approx 14.83$$ 8. Therefore, $x \approx 14.83$ cm. This assumes a right triangle with legs 6 cm and $x$ cm and hypotenuse 16 cm.