Pythagoras Theorem formula:
story, analogy and memory trick
The Pythagoras Theorem formula is a² + b² = c². In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
The Pythagoras Theorem formula
- a, bthe two shorter sides of a right-angled triangle
- cthe hypotenuse, opposite the right angle
The story
A ladder leans against a wall. The wall is one side, the ground is another, and the ladder is the longest side, the hypotenuse. A 5 m ladder with its foot 3 m from the wall reaches 4 m up the wall, because 3² + 4² = 5².
Real-life analogy
Think of crossing a rectangular park diagonally instead of walking along two edges. The shortcut is shorter, and its length comes from the formula.
Memory trick
Memorise the triples 3-4-5, 5-12-13 and 8-15-17, and their multiples. Spot one in a question and skip the calculation.
Exam tip
It works only for right-angled triangles. The hypotenuse is opposite the right angle and is always the longest side. Square each side first, then add.
Questions about Pythagoras Theorem
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