Let’s solve this step-by-step:

Problem Analysis:

1. Given:

   • The area of the rectangular field = 240 m².
   • One side of the rectangle = 10 m.
   • Speed of crossing diagonally = 25 m/minute.

2. Find:

   • The time it takes to cross the field diagonally.

Step 1: Find the dimensions of the rectangle.

The formula for the area of a rectangle is: $\text{Area} = \text{length} \times \text{width}$ Here, one side (width) is given as 10 m, so: $\text{length} = \frac{\text{Area}}{\text{width}} = \frac{240}{10} = 24 \, \text{m.}$ Thus, the dimensions of the rectangle are 10 m × 24 m.

Step 2: Calculate the diagonal of the rectangle.

The diagonal ($d$) of a rectangle can be calculated using the Pythagorean theorem: $d = \sqrt{(\text{length})^2 + (\text{width})^2}$ Substitute $\text{length} = 24 \, \text{m}$ and $\text{width} = 10 \, \text{m}$: $d = \sqrt{24^2 + 10^2} = \sqrt{576 + 100} = \sqrt{676} = 26 \, \text{m.}$

Step 3: Time to cross the field diagonally.

The time ($t$) it takes to cross the diagonal is: $t = \frac{\text{distance}}{\text{speed}}$ Substitute $\text{distance} = 26 \, \text{m}$ and $\text{speed} = 25 \, \text{m/min}$: $t = \frac{26}{25} = 1.04 \, \text{minutes.}$

Final Answer:

It will take approximately 1.04 minutes (or 62.4 seconds) to cross the field diagonally.

Would you like further details or explanations?

Related Questions:

1. How do you calculate the diagonal of any rectangular shape?
2. What is the relationship between area and perimeter in a rectangle?
3. How would the time change if the speed was halved?
4. What is the significance of the Pythagorean theorem in geometry?
5. How do you convert time in decimals (e.g., 1.04 minutes) into minutes and seconds?

Tip:

When solving problems involving geometry, always draw a quick diagram to help visualize the relationships between the given values.