Mon Prof Augmenté
The Squares on a Right Triangle
Age 13 · Maths
In a right-angled triangle, the longest side is called the hypotenuse, and it is always opposite the right angle. If you build a square on each side, the area of the biggest square is exactly the area of the two smaller squares added together.
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Age 13: open this week
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In the picture
- The right angle: the square corner where the two shorter sides meet
- Square on the side of length 3: area 3 × 3 = 9
- Square on the side of length 4: area 4 × 4 = 16
- Square on the hypotenuse, length 5: area 5 × 5 = 25, which equals 9 + 16
Examples
- A ladder leaning against a wall: knowing how high it reaches and how far its foot is from the wall tells you how long the ladder is.
- A TV screen’s size is measured along its diagonal, which you can work out from its width and height.
Key takeaways
- a² + b² = c², where c is the hypotenuse
- It only works for triangles with a right angle
Quiz: The Squares on a Right Triangle (Age 13)
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In a right-angled triangle, which side is the hypotenuse?
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In a right-angled triangle, the squares on the two shorter sides have areas of 9 and 16. What is the area of the square on the hypotenuse?
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Which triangles does the rule a² + b² = c² work for?
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