1. **State the problem:** We need to find the width $w$ of a rectangle given that its perimeter is 94 cm and its length is 19 cm. 2. **Write the formula for the perimeter of a rectangle:** $$P = 2L + 2W$$ where $P$ is the perimeter, $L$ is the length, and $W$ is the width. 3. **Substitute the known values into the formula:** $$94 = 2(19) + 2w$$ 4. **Simplify the equation:** $$94 = 38 + 2w$$ 5. **Isolate the term with $w$ by subtracting 38 from both sides:** $$94 - 38 = 2w$$ $$56 = 2w$$ 6. **Divide both sides by 2 to solve for $w$:** $$\frac{56}{\cancel{2}} = \frac{2w}{\cancel{2}}$$ $$28 = w$$ 7. **Final answer:** The width of the rectangle is 28 cm.