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. 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:
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} Multipliy 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 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
How to use the Rectangle Area and Diagonal CalculatorEnter 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 LinksRectangle Perimeter and Diagonal CalculatorOnline Geometry Calculators and Solvers. 