The width of the rectangle is 8 dm, which is 1/3 of its length. Find the perimeter and area of the rectangle.

Let the width of the rectangle be b and its length a.
By condition, the width is 8 dm, which is 1/3 of the length.
If one number is some part of another number, then this number is equal to the product of the second number by that very part, that is, if the number 8 is 1/3 of the unknown value, then the product of the unknown value and the fraction 1/3 will be equal to 8:
b = 1/3 * a;
1/3 * a = 8;
a = 8: 1/3;
a = 8 * 3/1;
a = 8 * 3;
a = 24 dm.
Thus, the length of the rectangle is 24 dm.
The area of ​​the rectangle is found by the formula:
S = a * b,
where a is the length of the rectangle, b is the width of the rectangle.
Substitute the known values ​​and find the area of ​​the rectangle:
S = 24 * 8;
S = 192 dm².
The perimeter of a polygon is equal to the sum of the lengths of all its sides. Since the opposite sides in a rectangle are equal, its perimeter can be found by the formula:
P = a + b + a + b = 2 * a + 2 * b = 2 * (a + b).
Substitute the known values ​​and find the perimeter of the rectangle:
P = 2 * (24 + 8);
P = 2 * 32;
P = 64 dm.
Answer: S = 192 dm²; P = 64 dm.