Beyond Rankers Academy
Building Minds, Not Just Rankers
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Beyond Rankers Academy
Building Minds, Not Just Rankers
Main site →
In a right-angled triangle, the square on the longest side equals the sum of the squares on the other two. Indian mathematicians wrote this down in the Baudhayana Sulbasutra centuries before Pythagoras.
The hypotenuse is the side opposite the right angle, and it is always the longest.
📐 Using it in three steps
Find the right angle. The side opposite it is the hypotenuse, c.
Write a² + b² = c² with the two shorter sides as a and b.
Substitute and solve. To find a shorter side, rearrange: a² = c² − b².
The Indian name comes first for a reason. The Baudhayana Sulbasutra, written around 800 BCE, states the rule for building altars — well before Pythagoras. NCERT names both.
It only works for right-angled triangles. If there is no right angle, a² + b² = c² is simply false. Check for the right angle before you start.
Some whole-number trios fit the theorem exactly. Learning them saves you the square-root working.
🔢 Triples worth memorising
| a | b | c | Check |
|---|---|---|---|
| 3 | 4 | 5 | 9 + 16 = 25 |
| 5 | 12 | 13 | 25 + 144 = 169 |
| 6 | 8 | 10 | 36 + 64 = 100 |
| 7 | 24 | 25 | 49 + 576 = 625 |
| 8 | 15 | 17 | 64 + 225 = 289 |
| 9 | 12 | 15 | 81 + 144 = 225 |
Multiples of a triple are also triples. From 3-4-5 you get 6-8-10, 9-12-15 and 30-40-50. If the numbers in a question look like a familiar triple scaled up, you can write the answer down immediately.
Ladders, shadows, diagonals and shortest paths are all the same triangle in disguise.
The classic ladder question: a ladder 13 m long leans against a wall with its foot 5 m away. How high does it reach? The ladder is the hypotenuse, so height² = 13² − 5² = 169 − 25 = 144, giving 12 m.
The diagonal of a rectangle splits it into two right triangles. For a 6 × 8 rectangle the diagonal is √(36+64) = √100 = 10. For a square of side a it is always a√2.
12 questions on right triangles. Find the hypotenuse first — it is opposite the right angle. 🍀