What is the perimeter of a square with area 576 m2, and what is the drawing area of a 100m x 50m field scaled at 1:1000?

The area of a square ($A$) is given by the formula $A = s^2$, where $s$ is the side length.
Given $A = 576 \text{ m}^2$.

$$s^2 = 576 \text{ m}^2$$

To find $s$, take the square root of the area:

$$s = \sqrt{576 \text{ m}^2}$$ $$s = 24 \text{ m}$$

The perimeter of a square ($P$) is given by the formula $P = 4s$.
Substitute the side length $s = 24 \text{ m}$:

$$P = 4 \times 24 \text{ m}$$ $$P = 96 \text{ m}$$

The correct option is C) $96 \text{ m}$.

The actual length ($L$) is $100 \text{ m}$ and the actual width ($W$) is $50 \text{ m}$.
The scale is $1:1000$, meaning 1 unit on the drawing represents 1000 units in reality.

Length on drawing ($L_d$):

$$L_d = \frac{\text{Actual Length}}{\text{Scale Factor}} = \frac{100 \text{ m}}{1000} = 0.1 \text{ m}$$

Width on drawing ($W_d$):

$$W_d = \frac{\text{Actual Width}}{\text{Scale Factor}} = \frac{50 \text{ m}}{1000} = 0.05 \text{ m}$$

The area of a rectangle ($A_d$) is given by $A_d = L_d \times W_d$.

$$A_d = 0.1 \text{ m} \times 0.05 \text{ m}$$ $$A_d = 0.005 \text{ m}^2$$

We know that $1 \text{ m} = 100 \text{ cm}$.
Therefore, $1 \text{ m}^2 = (100 \text{ cm})^2 = 10000 \text{ cm}^2$.

$$A_d = 0.005 \text{ m}^2 \times \frac{10000 \text{ cm}^2}{1 \text{ m}^2}$$ $$A_d = 50 \text{ cm}^2$$

The correct option is A) $50 \text{ cm}^2$.