Online calculator to calculate the dimensions (length and width) of a rectangle given the area A and perimeter P of the rectangle.
The formulas for the perimeter P and the area A of the rectangle are used to write equations as follows:
P = 2 * L + 2 * W
A = L * W
Then these equations are solved for L and W which are the length and width of the rectangle.
How to use the calculator
Enter the perimeter P and area A as positive real numbers and press "enter". The outputs are the width, length and diagonal of the rectangle. There are conditions under which this problem has a solution (see formulation of problem below).
Formulation of Problem
Let P be the perimeter of a rectangle and A its area. Let W and L be, respectively, the width and length of the rectangle. Find W and L in terms of P and A.
solution
P = 2 * W + 2 * L (1)
and
A = W * L (2)
solve equation (1) for W:
W = P / 2  L
and W by P / 2  L in A = W * L to obtain
A = L * (P / 2  L)
Rewrite as a standard quadratic equation in L
L^{ 2}  L (P / 2) + A = 0
Solve the above equation for L and find W using W = P / 2  L.
Practice: Find the discriminant of the above quadratic equation and find the condition on P and A under which the above problem has no solution.
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