P is the perimeter of a square and D is the diagonal of the square, choose the correct relation.

Correct option is D

Given:

P = Perimeter of the square

D = Diagonal of the square

Formula Used:

Perimeter of a square P = 4 × side

Diagonal of a square D =$$\text{side} \times \sqrt{2}$$​​

Solution:
Let the side of the square be s.

From the perimeter formula:

P = 4s

From the diagonal formula:

D =$$s \times \sqrt{2}$$​

s =$$\frac{D}{\sqrt{2}}$$​

Substitute this into the perimeter formula:

P = 4$$\times \frac{D}{\sqrt{2}} = 2\sqrt{2} \, D$$​