Question

A man is running around a hexagonal field of side length 6m, so that he always at a distance 3 metre from the nearest boundary. Find the length of path travelled by him in one round.

Answer 1

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Length = 300m

Breadth = 200m

Perimeter of rectangular park = 2 (l+b)

= 2 (300+200)m

= 2(500)m

= 1000m or 1 km.

Karan takes 4 round.

So distance covered by Karan = 4 × Perimeter

= 4 (1)

= 4 km

So he covered 4 km.

Number of round required to cover 9km = 9/Perimeter

= 9/1

= 9 rounds

So he should take 9 rounds to cover the distance of 9km.

Hope it helps.

Answer 2

Answer:

The length of the path travelled by the man in one round is 54.84m.

Step-by-step explanation:

Given a hexagonal field, means it has 6 sides.

The length of each side is 6m.

Thus the distance travelled by the man is,  $6\times 6=36m$

Also given that the man is always at a distance of 3m from the nearest boundary.

If the man runs always at a distance of 3m from the nearest boundary, then at the corners of the hexagon, he will be making a curved path.

Thus making a sector of an angle 60° at each corner of the hexagon.

Since, there are 6 corners in the hexagon, the sum of the 6 sectors will be a circle with radius 3 m.

Therefore, the the distance travelled by the man at the corners of the hexagon is equal to the circumference of the circle.

Circumference of the circle is given by

$2\pi r=2\times \dfrac{22}{7} \times 3\approx18.84m$

Therefore, the total distance travelled by the man is

$36+18.85=54.84m$

Hence, the length of the path travelled by the man in one round is 54.84m.

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