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:
*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}
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
The condition for the rectangle to exist is: * L ≥ √(2 A) *
__How to use the 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 Online Geometry Calculators and Solvers.
*
* |