8 women till 2 hectares in 5 days. How many hectares can 15 men till in 12 days if men and women work at the same rate? What is the perimeter of a room 6m by 4m?

5)

Step 1: Determine the work rate per person per day.
The work done is tilling farm land, measured in hectares.
Given: 8 women till 2 hectares in 5 days.
Work rate per person per day = $\frac{\text{Hectares}}{\text{Number of people} \times \text{Number of days}}$

$$\text{Rate} = \frac{2 \text{ hectares}}{8 \text{ women} \times 5 \text{ days}} = \frac{2}{40} \frac{\text{hectares}}{\text{person} \cdot \text{day}} = \frac{1}{20} \frac{\text{hectares}}{\text{person} \cdot \text{day}}$$

Step 2: Calculate the total hectares tilled by 15 men in 12 days using the same rate.
Assuming men and women work at the same rate.

$$\text{Hectares} = \text{Rate} \times \text{Number of people} \times \text{Number of days}$$ $$\text{Hectares} = \frac{1}{20} \frac{\text{hectares}}{\text{person} \cdot \text{day}} \times 15 \text{ men} \times 12 \text{ days}$$ $$\text{Hectares} = \frac{15 \times 12}{20} \text{ hectares}$$ $$\text{Hectares} = \frac{180}{20} \text{ hectares}$$ $$\text{Hectares} = 9 \text{ hectares}$$

15 men will till $\boxed{9 \text{ hectares}}$ of farm land.

6)
The room is a rectangle with length $6 \text{ m}$ and width $4 \text{ m}$.
The carpet is a rectangle with length $4 \text{ m}$ and width $3 \text{ m}$.