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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 L2 = x 2 + y 2 Substitute y by (P - 2 x) / 2 in the equation L2 = 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 L2 - 16 P 2 For the problem to have a solution, we must have the condition ? ? 0 satisfied. 128 L2 - 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. |
