The area of the rectangle is 25 cm ^ 2. Find the smallest possible perimeter of this rectangle.

Let x and y be the sides of the rectangle, then: x * y = 25 f (x, y) = 25 f (x, y) = 2 (x + y), x> 0, y> 0 y = 25 / x function and find the derivative of it: f (x) = 2 (25 / x + x) – name., x> 0 f ‘(x) = 2 (25 / x + x) – name., x> 0 Equate to zero: f ‘(x) = 0 25 / x ^ 2 = 1 System: x = 5, x = -5 x> 0 x = 5 Substitute: y = 25/5 = 5 f (5) = 2 (5+ 5) = 20 fnaim = f (5) = 20 (cm) [0; + infinite]
Answer: 20 cm