When is the area of a rectangle equal to the perimeter?

Area of the rectangle is the product of the length and the
width.

A = l*w

On the other
hand, the perimeter of the rectangle is:

P =
2(l+w)

Now, we'll put the area and the perimeter in the
relation of equality:

l*w =
2(l+w)

Now, we'll form the second degree equation, when
knowing the product and the sum of the length and
width.

x^2 - Sx + P = 0

We'll
use Viete's relations:

l + w =
S

l*w = P

But, l*w =
2(l+w)

P = 2S

x^2 - Sx + 2S =
0

delta = S^2 - 8S

S^2 - 8S =
0

S(S-8) = 0

S = 0
impossible

S = 8

l+w = 8
=> l = 8-w

l*w =
16

(8-w)*w - 16 = 0

w^2 - 8w +
16 = 0

w1 =
[8+sqrt(64-64)]/2

w = 4

l =
4