1. **State the problem:** We have a rectangle where the length $L$ is five times the width $W$, i.e., $L = 5W$. 2. The width $W$ is increasing at a rate of $\frac{dW}{dt} = 2$ cm/s. 3. We want to find the rate of increase of the area $A$ of the rectangle when $W = 5$ cm. 4. **Formula for area:** The area of a rectangle is given by $$A = L \times W$$ 5. Since $L = 5W$, substitute to get $$A = 5W \times W = 5W^2$$ 6. Differentiate both sides with respect to time $t$ to find the rate of change of area: $$\frac{dA}{dt} = 5 \times 2W \times \frac{dW}{dt} = 10W \frac{dW}{dt}$$ 7. Substitute $W = 5$ cm and $\frac{dW}{dt} = 2$ cm/s: $$\frac{dA}{dt} = 10 \times 5 \times 2 = 100$$ 8. **Answer:** The area is increasing at a rate of 100 cm$^2$/s when the width is 5 cm. **How to write the equation on Google Docs:** - Use the equation editor by clicking Insert > Equation. - Type the formula as $A = 5W^2$. - To show differentiation, type $\frac{dA}{dt} = 10W \frac{dW}{dt}$. - Substitute values and calculate step-by-step as shown above.