Question

How many times must I run around a square field, where the area is one hectare a distance of 6 kilometers?

Answer 1

Hint: The number of times I must run around a square field of one hectare to cover a distance of \[6\] kilometers means we have to calculate length and breadth. For this first convert the hectare into meters and kilometers into meters to make the calculation easy. Then calculate the side length of the square field with the help of the formula of area of the square. And after calculating the side length of the square, calculate the perimeter of the square by applying the formula of perimeter and then divide the distance which has to be covered by the perimeter of the square to calculate the number of times I must run.

Complete step by step solution:

The area of the square field is one hectare.

So, the area of the square field in \[{{\text{m}}^2}\],

$   = 6 \times 10000 $

$  = 60000{{\text{m}}^2} $

One hectare is equals to \[10000{\text{ }}{{\text{m}}^2}\]

The area that has to be covered is \[6\] kilometers.

So, the area that has to be covered in \[{\text{m}}\],

$  = 6 \times 1000 $

$   = 6000{\text{m}} $

One kilometer is equals to \[1000{\text{ m}}\]

As we know that the sides of the square are of the same length.

Let the length of the sides of the square is \[x\].

The area of the square field is:

$  {\text{A}} = {{length  \times  breadth}} $

$ 60000 = x \times x $

$  60000 = {x^2} $

$  \sqrt {60000}  = x $

$   \pm 244.94 = x $

As we know that the length of the sides cannot be negative so it will be positive. So,the length of side of the square is \[ + 244.94{\text{ m}}\].

The perimeter of the square is:

$   = 4 \times {\text{length of sides}} $

$   = 4 \times 244.94 $

$   = 979.76{\text{ m}} $

The number of times I must run around a square field:

$  = \dfrac{{{\text{The total area to be covered}}}}{{{\text{The perimeter of the square}}}} $

$   = \dfrac{{6000}}{{979.76}} $

$   = 6.12 $

$\therefore $ The number of times I must run around a square field of one hectare to cover a distance of \[6\] kilometers is \[6.12{\text{ times }}\] or \[6{\text{ times}}\].

Note:
In these types of questions, calculate perimeter whenever asked for distance traveled or length. Use basic formulas of area and perimeter. And always convert the units to make the calculations easy.