Study right-angled triangles and the theorem relating their sides — documented by the ancient Indian mathematician Baudhayana centuries before Pythagoras.
In a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides. This relationship was documented by Baudhayana in ancient India, and independently by Pythagoras in Greece.
A right triangle has legs 3 cm and 4 cm. Find the hypotenuse.
c² = 3²+4² = 9+16 = 25; c = 5 cm
A right triangle has hypotenuse 13 cm and one leg 5 cm. Find the other leg.
b² = 13²−5² = 169−25 = 144; b = 12 cm
A Pythagorean triple is a set of three whole numbers that satisfy a²+b²=c². Common triples like (3,4,5) and (5,12,13) appear frequently in geometry problems.
Verify that (6,8,10) is a Pythagorean triple.
6²+8² = 36+64 = 100 = 10², so yes
Is (7,24,25) a Pythagorean triple?
7²+24² = 49+576 = 625 = 25², so yes
1. A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
2. A right triangle has hypotenuse 17 cm and one leg 8 cm. Find the other leg.
3. Verify whether (9,12,15) is a Pythagorean triple.
4. A ladder 10 m long leans against a wall, its base 6 m from the wall. How high up the wall does it reach?
5. Is (5,6,8) a Pythagorean triple?