Dimensions Of A Rectangle
Find the length and width of a rectangle given its area and perimeter. Free online geometry solver for students, architects, and construction professionals.
About This Calculator
The Rectangle Dimensions Calculator finds the length and width of a rectangle when you know its area and perimeter. Given area A and perimeter P, the calculator solves the system L x W = A and 2(L + W) = P using the quadratic formula to return both dimensions.
Frequently Asked Questions
How do you find the dimensions of a rectangle given area and perimeter?
If area = A and perimeter = P, then L = (P/4) + sqrt(P^2 - 16A)/4 and W = (P/4) - sqrt(P^2 - 16A)/4.
What if P^2 - 16A is negative?
No real rectangle exists with the given area and perimeter. The maximum area for a given perimeter is P^2/16 (a square).
What is the relationship between area and perimeter of a rectangle?
For a fixed perimeter, a square maximizes the area. For a fixed area, a square minimizes the perimeter.
Is this calculator free?
Yes, all calculators on Calculy are completely free to use.