Specify the size of the sides of the rectangle if the perimeter is 26cm and the area is 12cm2.

Here are the necessary formulas for the calculations: Perimeter (P) of the rectangle: P = 2 * (a + b); area (S) of the rectangle: S = a * b, where a and b are the sides of this rectangle.
According to the conditions of the assignment, we have P = 2 * (a + b) = 26 cm and S = a * b = 12 cm2.
Thus, we get two equalities a + b = 13 and a * b = 12 (we will omit the units for now).
According to Vieta’s theorem, taking into account the last equalities, we can assert: a and b are the roots of the following reduced equation: x ^ 2 – 13 * x + 12 = 0.
Let’s solve the last quadratic equation. Let’s calculate the discriminant D = (–13) ^ 2 – 4 * 1 * 12 = 169 – 48 = 121> 0. Therefore, we get two roots х1 = (13 –√ (121)) / 2 = (13 – 11) / 2 = 2/2 = 1 and x2 = (13 + √ (121)) / 2 = (13 + 11) / 2 = 24/2 = 12.
Thus, the rectangle has sides of 1 cm and 12 cm.
Answer: 1 cm and 12 cm.