
An online calculator to calculate the length and width (dimensions) of a rectangle given its perimeter P and length of diagonal L. If x and y are the length and width of a rectangle, the perimeter P 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 P = 2 x + 2 y for y to obtain y = (P  2 x) / 2 Square both sides of the equation L = √ (x^{ 2} + y^{ 2}) to obtain L^{2} = x^{ 2} + y^{ 2} Substitute y by (P  2 x) / 2 in the equation L^{2} = x^{ 2} + y^{ 2} to obtain L^{ 2} = x^{ 2} + ((P  2 x) / 2) ^{ 2} L^{ 2} = x^{ 2} + (P  2 x)^{ 2} / 4 Multipliy all terms of the above equation by 4, simplify and write it in standard for to obtain 8x^{ 2}  4 P x + P^{ 2}  4L^{ 2} = 0 Discriminant of above equation ? = (4 P)^{2}  4(8)(P^{ 2}  4L^{ 2}) = 128 L^{2}  16 P^{ 2} For the problem to have a solution, we must have the condition ? ? 0 satisfied. 128 L^{2}  16 P^{ 2} ? 0 Given P and L, once you solve the above equation for x, you also have to ckeck that y = (P  2 x) / 2 is positive.
How to Use the Rectangle Perimeter and Diagonal CalculatorEnter the perimeter P 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 Area and Diagonal CalculatorOnline Geometry Calculators and Solvers. 