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Pythagorean Theorem Calculator — a² + b² = c²
Solve for the missing hypotenuse or leg of any right triangle with area and perimeter.
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More in Mathematics & Statistics:
Right Triangle Sides
Pythagorean Equation
Transparent mathematical methodology explained in plain English.
a² + b² = c² => c = √(a² + b²), a = √(c² - b²) In any right-angled triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
Variables Explained:
- a, b: Lengths of the two legs perpendicular to each other.
- c: Length of the hypotenuse (opposite the 90° angle).
Real Project Example
Finding Hypotenuse for Legs 6 ft and 8 ft
Classic 3-4-5 proportional triangle.
Sample Project Inputs:
Side a: 6 ft
Side b: 8 ft
Step-by-Step Calculation:
- a² = 6² = 36.
- b² = 8² = 64.
- a² + b² = 36 + 64 = 100.
- c = √100 = 10 ft.
- Perimeter = 6 + 8 + 10 = 24 ft.
- Area = 0.5 × 6 × 8 = 24 sq ft.
Calculated Answer: Hypotenuse c = 10 ft; Area = 24 sq ft.
Knowledge Base
Frequently Asked Questions: Pythagorean Theorem
Click any question below to expand quick answers, formulas, and expert tips.
Can the hypotenuse ever be shorter than a leg?
No. The hypotenuse is always opposite the largest angle (90 degrees) and is strictly the longest side of a right triangle.