What are the sides of the rectangle if the area is 12 cm, and the perimeter is 26 cm.

Let a and b be the sides of the rectangle. Then, based on the data of the problem, you can formulate the following two equations:

ab = 12,

2a + 2b = 26.

Let us express from the second equation a:

2a + 2b = 26,

2a = 26 – 2b,

a = (26 – 2b) / 2,

a = 13 – b.

Substitute this expression for a into the first equation and solve it:

(13 – b) * b = 12,

13b – b² = 12,

b² – 13b + 12 = 0,

D = (- 13) ² – 4 * 1 * 12 = 169 – 48 = 121,

b1,2 = (13 ± √121) / (2 * 1),

b1,2 = (13 ± 11) / 2,

b1 = (13 + 11) / 2, b2 = (13 – 11) / 2,

b1 = 12, b2 = 1.

It makes no sense to search for a, since the results will be a mirror image of those obtained. This means that the sides of this rectangle are 12 cm and 1 cm.

Answer: the sides of the rectangle are 12 cm and 1 cm.