​A fence is constructed along the diagonal of a square field. What is the length of the fence (in km) if the area of the square field is $$2 \, \text{km}^2$$​?​

Correct option is A

Given:

Area of the square field = 2 km²

Formula Used:

Area of a square = side $$\times$$​side

Diagonal of a square = $$\sqrt 2$$​ $$\times$$​ side

Solution:

the side length of the square:

​$$\text{Side} = \sqrt{\text{Area of square}}$$​​

Side = $$\sqrt 2$$ km​

the length of the diagonal:

Diagonal = $$\sqrt 2$$ $$\times$$​​side

Diagonal = $$\sqrt 2$$ $$\times \sqrt 2$$ km​

Diagonal = 2 km

Therefore, the length of the fence along the diagonal of the square field is 2 kilometers.

Option (A) is right answer.