Area = A = x y
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:
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 L2 = x 2 + y 2
Substitute y by A / x in the equation L2 = 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 = (-L2)2 - 4(1) A 2
The problem of finding x and y has a solution if Δ ≥ 0
L4 - 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.
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