The rectangle has an area of 55 cm2 and a perimeter of 36 cm. Find the sides of this rectangle?

We denote by x and y the sides (in cm) of the rectangle.
The area (S) of a rectangle can be calculated using the formula S = a * b, where a and b are the sides of the rectangle. We have x * y = 55 cm2.
The perimeter (P) of the rectangle is calculated by the formula P = 2 * (a + b). We have 2 * (x + y) = 36 cm.
Since y = 18 – x, we have: x * (18 – x) = 55 or x ^ 2 – 18 * x + 55 = 0.
The last quadratic equation has 2 roots: x1 = 9 + √26 and x ^ 2 = 9 – √26.
Therefore, y1 = 9 – √26 and y2 = 9 + √26
Answer: (9 + √26) cm; (9 – √26) cm.