The width of the rectangle is 3.2 times less than the length, and the perimeter is 105 meters.

The width of the rectangle is 3.2 times less than the length, and the perimeter is 105 meters. Find the perimeter and area of a square with a side equal to the width of this rectangle.

To solve this problem, you need to write an equation. The perimeter of a rectangle is the sum of the lengths of all its sides. Since the opposite sides in a rectangle are equal, then P = 2 * (a + b), where a is the length, b is the width. Let the width be x, then the length is 3.2x. Knowing that the perimeter is 105 meters, let’s make an equation.
2 * (x + 3.2x) = 105;
2 * 4.2x = 105;
8.4x = 105;
x = 105 / 8.4;
x = 12.5 cm.
Since all sides of a square are equal, its perimeter is P = 4a, where a is its side. The area of ​​a square is equal to the square of its side. S = a ^ 2. We calculate the perimeter and area, knowing that the side is 12.5 cm.
P = 4 * 12.5 = 50 cm.
S = 12.5 * 12.5 = 156.25 cm ^ 2.
Answer: 50 cm, 156.25 cm ^ 2.