Question

If to complete 2 rounds of a square field, Ajay travels 360 m, then find the area of the field.

Answer 1

Hint: In order to solve this problem, we need to know the formula for the perimeter of the square. The formula for the perimeter of the square is the sum of all four sides. We also need to find the formula of the area of the square. The formula for the area of the square is ${{\left( side \right)}^{2}}$ . We need to find the side of the square using the condition of the perimeter and then using the side of the square we need to find the area of the square.

Complete step-by-step solution:
We have given a square field and a person travels around the field in 2 rounds and covers 360m.
That means that the person is traveling the perimeter of the square twice and covers the distance of 360m.
We can first draw the diagram and understand it better.

We know that all the sides of the square are equal.
Let the side of the square be $x$ m.
Now, we need to find the perimeter of the square.
There are four sides of the square.
Therefore, the perimeter of the square is the sum of all four sides, we get,
Perimeter of the square is $x + x + x + x = 4x$.
Now, we are given that the person travels two times around the field.
Therefore, we need to multiply the perimeter by 2 and equate to 360.
We get,
$2\times 4x=360$
Solving this equation for x we get,
$x=\dfrac{360}{8}=45m$ .
The side of the field is $45m$.
Now, we find the area of the square field.
The formula for the area of a square field is ${{\left( side \right)}^{2}}$ .
Substituting the values, we get,
Area of the square field = ${{45}^{2}}=2025{{m}^{2}}$.

Note: In this problem, we need to understand that the person travels for two rounds around the field and so we need to multiply the perimeter by 2. Also, while calculating the perimeter we need to add all the sides of the square and while finding the area, we need to find the product of only two sides of the square.