Dimensions of Rectangle Calculator
Find rectangle length and width from area, perimeter, or one known dimension
Calculate Rectangle Dimensions
Area = length × width
Perimeter = 2(length + width)
Example Problems
Example 1: From Area and Perimeter
Problem: A rectangle has an area of 24 cm² and a perimeter of 20 cm. Find its dimensions.
Solution:
• Using the quadratic formula: a² - (P/2)×a + A = 0
• a² - 10a + 24 = 0
• a = [10 ± √(100 - 96)] / 2 = [10 ± 2] / 2
• Answer: Length = 6 cm, Width = 4 cm
Example 2: From Length and Area
Problem: A rectangle has a length of 8 inches and an area of 32 square inches. Find the width.
Solution:
• Formula: Width = Area ÷ Length
• Width = 32 ÷ 8 = 4 inches
• Answer: Width = 4 inches
Example 3: From Width and Perimeter
Problem: A rectangle has a width of 3 meters and a perimeter of 16 meters. Find the length.
Solution:
• Formula: Length = (Perimeter ÷ 2) - Width
• Length = (16 ÷ 2) - 3 = 8 - 3 = 5 meters
• Answer: Length = 5 meters
Rectangle Formulas
Basic Formulas
• Area = length × width
• Perimeter = 2(length + width)
• Diagonal = √(length² + width²)
From Area & Perimeter
• Quadratic: a² - (P/2)×a + A = 0
• Solution: a = [(P/2) ± √((P/2)² - 4A)] / 2
• Length = larger solution
• Width = smaller solution
Rectangle Properties
Opposite sides equal
Length sides are equal, width sides are equal
All angles 90°
Four right angles in every rectangle
Special case: Square
When length = width
Diagonals equal
Both diagonals have same length
Understanding Rectangle Dimensions
What are Rectangle Dimensions?
Rectangle dimensions refer to the length and width of a rectangle. These are the two unique measurements that completely define the size and shape of any rectangle. The length is typically the longer side, and the width is the shorter side.
Why Find Dimensions?
- •Construction and architecture planning
- •Material calculation and cost estimation
- •Engineering design and specifications
- •Geometry and mathematical problem solving
Mathematical Approach
Method 1: Area & Perimeter
• Set up: P = 2(a + b), A = a × b
• Substitute: b = P/2 - a
• Form quadratic: a² - (P/2)a + A = 0
• Solve using quadratic formula
Method 2: One Known Dimension
• From area: other = A ÷ known
• From perimeter: other = P/2 - known
• Direct calculation method
Important Notes
- • Solutions must be positive real numbers
- • Check if area and perimeter are physically possible
- • For squares: length = width
- • Diagonal follows Pythagorean theorem