The sides of the rectangle are 2 to 6, and its perimeter is 32 cm. Find the area of this rectangle.

1. Take one part of the length equal to x cm, so the width of the rectangle is 2 * x cm.
2. In turn, the length of the rectangle is x * 6 cm.
3. The perimeter of a rectangle (P) is the sum of the lengths of all its sides. We can write the equation for finding the perimeter as P = 2 * (2 * x + 6 * x) cm.
4. According to the condition of the posed problem, P is equal to 32 cm. Let us solve the equation of point 3, substituting P:
32 = 2 * (2 * x + 6 * x);
32 = 2 * 8 * x;
32 = 16 * x;
x = 2.
5. The width is 2 * x = 2 * 2 = 4 m, the length is 2 * 6 = 12 cm.
6. Area of ​​a rectangle (S) – the product of its width and length. Then the area is S = 4 * 12 = 48 cm squared.
Answer: The area of ​​the rectangle is 48 cm squared.