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maths · 30 seconds

Why the 3–4–5 triangle works

A visual route from squares to a right angle.

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What is the hypotenuse when the perpendicular sides are 6 and 8?

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Illustrations generated with OpenArt. Narration uses free local Kokoro neural voices. Illustrations are visual aids; the written lesson carries the explanation.

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Build three squares

Draw a right triangle with perpendicular sides 3 and 4. Build a square on each side.

3² + 4²

Count the area

The small squares have areas 9 and 16. Together that is 25 square units.

9 + 16 = 25

Find the long side

The square on the hypotenuse has area 25. Its side is the square root of 25: 5.

√25 = 5

Check the condition

The formula applies to right triangles. The hypotenuse is always opposite the right angle.

a² + b² = c²

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