# 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*to obtain

^{ 2}+ y^{ 2})*L*

^{2}= x^{ 2}+ y^{ 2}Substitute

*y*by

*A / x*in the equation

*L*to obtain

^{2}= x^{ 2}+ y^{ 2}*L*

^{ 2}= x^{ 2}+ (A / x )^{ 2}Multiply all terms of the above equation by

*x*, simplify and write it in standard for to obtain

^{ 2}x

^{ 4}-

*L*= 0

^{ 2}x^{ 2}+ A^{ 2}Discriminant of above equation

Δ = (-L

^{2})

^{2}- 4(1) A

^{ 2}

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

L

^{4}- 4 A

^{ 2}≥ 0

*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 CalculatorOnline Geometry Calculators and Solvers .