The area of the rectangle is 420 cm ^ 2, and its perimeter is 94m. Find the lengths of the sides of the rectangle.

Suppose that one of the sides of the rectangle is equal to x, and the second is equal to y, then the condition of the problem can be written as follows:

2 * (x + y) = 94,

x * y = 420.

From the first equation we get:

x + y = 94: 2,

y = 47 – x.

Substitute this value into the second equation:

x * (47 – x) = 420,

47 * x – x² = 420,

x² – 47 * x + 420 = 0.

The discriminant of this equation is:

(-47) ² – 4 * 1 * 420 = 529.

The equation has the following roots:

x = (47 – 23) / 2 = 12 and x = (47 + 23) / 2 = 35.

Therefore, the second side is equal to:

47 – 12 = 35 or 47 – 35 = 12.

Answer: 35 and 12.