The length of the rectangular section is 12 cm greater than its width, which is equal to the length of this section

The length of the rectangular section is 12 cm greater than its width, which is equal to the length of this section, if the area of the section is 60, denote the length of the section as x.

Because the area is the product of the sides, so one of the sides is equal to the area divided by the second side. Let x cm be the length of the rectangle, then if the area is 60 cm2, 60 / x cm is the width of this rectangle. According to the condition of the problem, the difference between the sides is 12 cm, we get the correct equality:

x – 60 / x = 12,

x ^ 2 – 60 = 12x,

x ^ 2 – 12x – 60 = 0,

D = b ^ 2 – 4ac

D = 144 – 4 * (-60) = 384.

x = (-b ± √D) / 2a

x = (12 ± 8√6) / 2

x1 = 6 + 4√6, x2 = 6 – 4√6.

The second value is negative, so the root is only x1 = 6 + 4√6.

The second side is: 60 / (6 + 4√6).

Answer: the sides of the rectangle are 6 + 4√6 cm and 60 / (6 + 4√6) cm.