# Rectangle Area and Diagonal Calculator

An online calculator to calculate the length and width (dimensions) of a rectangle given its area A and length of diagonal L is presented. If x and y are the length and width of a rectangle, the area A and the length L of the diagonal may be expressed in terms of x and y as follows:

*Area = A = x y*

*length of diagonal = L = √ (x*^{ 2} + y^{ 2})

The calculator in this page solves the above equations in two variables and display the length and width.

solve *A = x y* for *y* to obtain *y = A / x *

Square both sides of the equation *L = √ (x*^{ 2} + y^{ 2}) to obtain *L*^{2} = x^{ 2} + y^{ 2}

Substitute *y* by * A / x * in the equation *L*^{2} = x^{ 2} + y^{ 2} to obtain

*L*^{ 2} = x^{ 2} + (A / x )^{ 2}

Multiply all terms of the above equation by *x*^{ 2}, simplify and write it in standard for to obtain

x^{ 4} - *L*^{ 2} x^{ 2} + A^{ 2} = 0

Discriminant of above equation

? = (-L^{2})^{2} - 4(1) A^{ 2}

The problem of finding x and y has a solution if ? ? 0

L^{4} - 4 A^{ 2} ? 0

The condition for the rectangle to exist is: * L ? √(2 A) *

## How to use the Rectangle Area and Diagonal Calculator

Enter the area A and the length L of the diagonal of the rectangle to solve, as positive real numbers, and press "calculate". The outputs are the dimensions, length x and width y, of the rectangle.

## More References and Links

Rectangle Perimeter and Diagonal Calculator

Online Geometry Calculators and Solvers.