Understanding the Problem
To form a rectangle using a piece of string that is 60 cm long, we need to understand the relationship between the perimeter, length, and breadth of the rectangle. The perimeter (P) of a rectangle is given by the formula:
P = 2(length + breadth)
In this case, the perimeter is 60 cm.
Calculating Length and Breadth
Using the perimeter formula, we can derive the relationship between length (L) and breadth (B):
- Rearranging the formula gives us:
L + B = 30 cm
This means the sum of the length and breadth must equal 30 cm.
Possible Combinations
Now, we can find various combinations of length and breadth:
- If L = 1 cm, then B = 29 cm
- If L = 5 cm, then B = 25 cm
- If L = 10 cm, then B = 20 cm
- If L = 15 cm, then B = 15 cm (this is a square)
- If L = 20 cm, then B = 10 cm
- If L = 25 cm, then B = 5 cm
- If L = 29 cm, then B = 1 cm
Conclusion
The possible pairs of length and breadth can be summarized as:
- (1 cm, 29 cm)
- (5 cm, 25 cm)
- (10 cm, 20 cm)
- (15 cm, 15 cm)
- (20 cm, 10 cm)
- (25 cm, 5 cm)
- (29 cm, 1 cm)
Each combination maintains the perimeter of 60 cm while offering different dimensions for the rectangle.