Length and Width of Rectangle Given Perimeter Calculator
Find the unknown dimensions of a rectangle when perimeter and one side are known
Calculate Rectangle Dimensions
Total distance around the rectangle
The measurement of one side
Rectangle Dimensions
Example Calculations
Example 1: Find Unknown Side
Problem: A rectangle has a perimeter of 20 m and a width of 3 m. Find the length.
Given: Perimeter = 20 m, Width = 3 m
Solution Steps
1. Use formula: Length = (P/2) - Width
2. Substitute values: Length = (20/2) - 3
3. Calculate: Length = 10 - 3 = 7 m
4. Answer: Length = 7 m, Width = 3 m
5. Verify: P = 2(7 + 3) = 20 m ✓
Example 2: Square Calculation
Problem: A square has a perimeter of 16 cm. Find all sides.
Solution: Side = P/4 = 16/4 = 4 cm
Answer: All sides = 4 cm each
Key Formulas
Rectangle Perimeter
P = 2(L + W)
P = 2L + 2W
Find Length
L = (P/2) - W
Find Width
W = (P/2) - L
Square Side
s = P/4
Quick Tips
You need either one side OR know it's a square
Known side must be less than half the perimeter
For a square, all sides are equal: P/4
Rectangle: opposite sides are equal
Understanding Rectangle Perimeter Calculations
Basic Concepts
A rectangle's perimeter is the total distance around its edge. To find unknown dimensions, you need at least one known side in addition to the perimeter.
Why One Side is Needed
Without knowing at least one side, there are infinite possible rectangles with the same perimeter:
- • 10×0 rectangle: P = 20
- • 8×2 rectangle: P = 20
- • 6×4 rectangle: P = 20
- • 5×5 square: P = 20
Solution Methods
Method 1: Known Side
Use P = 2(L + W) to find the unknown dimension
Method 2: Square
When all sides are equal, use P = 4s
Validation
Always verify your answer by calculating the perimeter using your results. The calculated perimeter should match the given perimeter.
Special Cases
Square Recognition
If your calculation results in length = width, you've found a square! This happens when the unknown side equals the known side.
Invalid Results
If the known side is greater than or equal to half the perimeter, no valid rectangle exists.