Question

The area of a square garden is 200 m². How long is the diagonal?

Answer 1

Let s = side length of square, then
200=s^2, or
s=sqrt(200)=sqrt(2*10^2)=10sqrt(2)
The diagonal turns out to be sqrt(s^2+s^2) by the Pythagoras theorem and equals sqrt(2s^2)=s*sqrt(2) = 10sqrt(2)*sqrt(2)=10*2=20.

In general, the diagonal D of a square with area A is given by
D=sqrt(2)*sqrt(A)=sqrt(2A)
In the case given it is Diagonal length = sqrt(2*200)=sqrt(400)=20 (as before)