Popular: 1/2 + 3/4 20% of 150 GCF(12, 18) 100 ÷ 7 √144 Circle r=7 sin(30°) 255 in Binary
Geometry & Triangles • Lesson 23 ⏱ 6 min read 📅 Updated Nov 2026

The Pythagorean Theorem (a² + b² = c²): How to Solve Right Triangles

Understand the Pythagorean theorem, identify the hypotenuse, solve for missing leg lengths, and discover common Pythagorean Triples (3-4-5, 5-12-13).

Core Theorem

In any right-angled triangle, the area of the square built on the hypotenuse equals the sum of the areas of the squares on the other two legs!

a = 3 b = 4 c = 5 3² + 4² = 9 + 16 = 25 = 5²
Right Triangle Geometry: a² + b² = c² (Hypotenuse c is Always Longest)

The 4 Famous Pythagorean Triples

Triple (a, b, c)Verification (a2 + b2 = c2)Common Scaled Multiples
3 – 4 – 59 + 16 = 256-8-10, 9-12-15, 30-40-50
5 – 12 – 1325 + 144 = 16910-24-26
8 – 15 – 1764 + 225 = 28916-30-34
7 – 24 – 2549 + 576 = 62514-48-50
Try It Yourself

Practice with Our Interactive Pythagorean Theorem Calculator

Check your calculations or explore full step-by-step solutions instantly.

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Solved Step-by-Step Examples:Hypotenuse of 3 and 4Triangle Calculator
Your Turn!

Check Your Understanding (3 Quick Questions)

Score: 0 / 3

Question 1: In a right triangle with legs a = 6 and b = 8, what is hypotenuse c?

Question 2: Which side of a right triangle is the hypotenuse?

Question 3: Which of these is a famous Pythagorean Triple?