The area of a square field is 8 hectares. It would take a man take to cross it diagonally by walking at the rate of 4 kmph is ____ minutes.

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Concept: The man will take 6 min to cross the diagonal. The area of a square is equal to the square of its side, and the diagonal of a square is

\sqrt{2}

times its side. Calculate the sides of a square box by its area, and the length of the diagonal by the length of the sides. Now that we know the man's distance traveled and his speed, we can easily calculate the required time using the following formula:

t = \frac{d}{s}

We know that the area of the forecourt is equal to the forecourt of its side. Let a be the side of the square field and d be it's slant
Now, the formula for area of the square field will be

And, the given area of a square field is 8 hectares. Now, we need to convert the given area from hectares to square kilometers. We know that 1 hectare is equal to0.01 square kilometers. Therefore, 8 hectares is equal to

square kilometers
Now, for the given square field, we've

Taking square root both sides

Therefore, the side of square field

km
Now, we know that slant of a forecourt is

times its side,
Thus, the slant of the square field is

times the side of the square field. Let d be the slant of a square field,

Now, to calculate the time a man would take to cross the field transversely by walking at the rate of 4 kmph, we need to know the relation between speed, time and distance, covered by an object. Speed is equal to distance divided by time.
Time is equal to distance divided by the speed
Let t be the time the man would take to cross the field transversely
And the speed of man as given is 4 kmph, the distance he has to cover is the slant of the field. The distance is

km
Thus, according to the formula

Now we know that there are 60 twinkles per hour
Thus

Hence, it takes a man 6 twinkles to walk transversely across the field at a speed of 4 km/h.

The area of a square field is 8 hectares. It would take a man take to cross it diagonally by walking at the rate of 4 kmph is ____ minutes.

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