The area of a square field is 576 `km^(2)`. How long will it take for a horse to run around at the speed of 12 km/h ?

Options

A. 12 h
B. 10 h
C. 8 h
D. 6 h

Answer

To solve the problem step by step, we need to determine the time it takes for a horse to run around a square field given its area and the horse's speed.

### Step 1: Find the side length of the square field.
The area of a square is given by the formula:
\[ \text{Area} = \text{side}^2 \]
Given that the area is 576 km², we can find the side length by taking the square root of the area:
\[ \text{side} = \sqrt{576} = 24 \text{ km} \]

### Step 2: Calculate the perimeter of the square field.
The perimeter (P) of a square is calculated using the formula:
\[ P = 4 \times \text{side} \]
Substituting the side length we found:
\[ P = 4 \times 24 = 96 \text{ km} \]

### Step 3: Calculate the time taken to run around the field.
We know the speed of the horse is 12 km/h. To find the time (T) taken to cover the perimeter, we use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the values we have:
\[ T = \frac{96 \text{ km}}{12 \text{ km/h}} = 8 \text{ hours} \]

### Final Answer:
It will take the horse 8 hours to run around the square field.

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