Find the perimeter of a rectangle with a diagonal of 20 cm and an area of 196 cm2.

Take the x and y sides of the rectangle, then
x * y = 196 by area definition.
x ^ 2 + y ^ 2 = 20 ^ 2 by the Pythagorean theorem.
Let us express x from the first equation:
x = 196 / y
substitute in the second:
(196 / y) ^ 2 + y ^ 2 = 400
196 ^ 2 + y ^ 4 = 400 * y ^ 2
y ^ 2 = (400 + -√16000-4 * 196) / 2 = 144
x ^ 2 = 400-144 = 256
Then y = 12, x = 16
The perimeter will be equal to:
2 * (12 + 16) = 56.