The area of the rectangle is 31 whole 9/20 dm squared, its length is 4 whole 1/4 dm. Find the pyrimeter of the rectangle.

1. Let’s find the width of the rectangle if, according to the condition, its length is 4 1/4 dm², and the area is 31 9/20 dm²:
S = a * b, where S = 31 9/20 dm² a = 4 1/4 dm.
Let’s convert the mixed number to an improper fraction:
S = 31 9/20 = 629/20 dm²;
a = 4 1/4 = 17/4 dm;
17/4 * b = 629/20;
b = 629/20 * 4/17 = 37/5 = 7 2/5;
b = 7 2/5;
Therefore, the width of the rectangle is 7 2/5 dm.
2. Find the perimeter of the rectangle if it is the sum of all its sides:
P = 2 (a + b);
P = 2 * (17/4 + 37/5) = 2 * (17/4 * 20/20 + 37/5 * 20/20) = 2 * ((17 * 5 + 37 * 4) / 20) = 2 ((85 + 148) / 20) = 2 * 233/20 = 23.3 dm.
Answer: perimeter 23.3 dm.