Question

What is an equation for the perimeter of a square, p, as a function of its area, a?

Answer 1

Let side of square is x.
So we can say area of square is = (side) * (side)
So we can say area =
`x * x = x^2`
But as given area is a.
So we can write

`a = x^2`
Now we can find value of x as

`x = √(a)` .......................................................(i)

In general perimeter of square = 4 * side
SO the perimeter will be =
`4*x = 4x`
But is given perimeter is p.
So we can write

`p = 4x`

Now we can place value of x in this


`p = 4 √(a)`