Given the area of a rectangle and it's aspect ratio (width over height), how can I calculate the lengths of it's sides?

Question

Given the area of a rectangle and it's aspect ratio (width over height), how can I calculate the lengths of it's sides?

Answer 1

(i)   A = wh

(ii)  r = w/h

 

You want both w and h in terms of A and r.

 

(i) ⇒ h = A/w

 

Plug this into (ii).

 

r = w/(A/w) = w²/A

 

w = √(rA)

 

Plug this w into (i).

 

A = h√(rA)

 

h = √(A/r)