Question

The area of a square field is $4$ hectares and finds the length of its side?

Answer 1

Hint: Before solving this question, let's get familiar with the units used in the question. As you may know, hectare is the unit used to specify area. You should simplify (change) the unit in order to make your calculations error free. And thus \[1{\text{ hectare}} = 10,000{m^2}.\] Hence, the shape of the field is mentioned to be square. We know that area of square$ = {(a)^2}$,where 'a' is the side of that square.

Complete step-by-step solution:
We are given that the area of a square field \[ = 4\] hectares. All we need is to find the length of the square field.
We know that,
\[1{\text{ hectare}} = 10,000{m^2}\]
Therefore \[4{\text{hectares}} = 4 \times 10,000{m^2} = 40,000{m^2}\]
Suppose 'x' is the length of a square field. Now, by the formula of area of square,
\[ \Rightarrow {x^2} = 40,000{m^2}\]
Taking square root both sides, we will get
\[
   \Rightarrow \sqrt {{x^2}} = \sqrt {40,000} m \\
   \Rightarrow x = \pm 200m \\
 \]
But, here we are finding the length of the side, and it is not possible that the length of a side being negative also makes no sense. So we will take only positive values and reject the negative one. Then we will get
\[ \Rightarrow x = 200m\]

Therefore the length of sides of the square field is \[200m\]

Note: Whenever you change the unit of any quantity that is given in the question in order to simplify your calculations, does not forget to change it back to the same unit mentioned in the question. Also you may think that the question is given in hectare units then why we have answered it in meters, it is so because hectare is a specific unit which only measures area.