The width of the rectangle is 9 dm and the length is 2 dm longer.

The width of the rectangle is 9 dm and the length is 2 dm longer. Find the area of a square with the same perimeter as the given rectangle.

Let’s find the length of the rectangle:
a = 9 + 2 = 11 (dm).
Now we can calculate the perimeter of the rectangle:
P = 2 * (a + b) = 2 * (9 + 11) = 40 (dm).
The perimeter of the square is P = 4 * a. Find the side of the square:
40 = 4 * a,
a = 40: 4,
a = 10 (dm).
Knowing the size of the side of a square, we can calculate its area:
S = a² = 10² = 100 dm².
Answer: S = 100 dm².