1. **State the problem:** We are given a rectangle whose width is thrice the length, and the width is equal to the side of a square. 2. **Define variables:** Let the length of the rectangle be $L$. Then width of the rectangle = $3L$. 3. Let the side of the square be $S$. Given, width of rectangle equals the side of the square: $$3L = S$$ 4. From this, the side of the square $S$ depends on the length $L$ of the rectangle. 5. Without additional information about length $L$ or the area, we can establish the relationship: - Rectangle dimensions: length $L$ and width $3L$ - Square side: $3L$ 6. Observations: - The rectangle has a longer width than length. - The square's side equals the rectangle's width. - The perimeter of rectangle = $2(L + 3L) = 2(4L) = 8L$ - The perimeter of square = $4S = 4(3L) = 12L$ 7. Therefore, the square has a greater perimeter than the rectangle. 8. The area of rectangle = $L \times 3L = 3L^2$ The area of square = $S^{2} = (3L)^2 = 9L^2$ Square area is three times the rectangle area. **Final conclusion:** The side of the square equals the width of the rectangle, which is thrice its length. The square's area is three times the rectangle's area, and the square has a larger perimeter.