# 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 is presented. 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 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

Multiply 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

? = (-L2)2 - 4(1) A 2

The problem of finding x and y has a solution if ? ? 0

L4 - 4 A 2 ? 0

The condition for the rectangle to exist is: L ? √(2 A)

## How to use the Rectangle Area and Diagonal 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.

 A = 15 L = 12 x (length) = y (width) =