a^2 + b^2 = c^2, where c is the length of the hypotenuse.

A Pythagorean triple consists of 3 integers which satisfies the Pythagorean Theorem.

There are 12 such triples in which c < 100. For all practical purposes you need not memorize all of theses, but many times the tiples up to (11, 60, 61) are seen frequently. It helps to memorize those.

( 3 , 4 , 5 ) | ( 5, 12, 13) | ( 7, 24, 25) | ( 8, 15, 17) |

( 9, 40, 41) | (11, 60, 61) | (12, 35, 37) | (13, 84, 85) |

(16, 63, 65) | (20, 21, 29) | (28, 45, 53) | (33, 56, 65) |

(36, 77, 85) | (39, 80, 89) | (48, 55, 73) | (65, 72, 97) |

Pythagoras theorem is very helpful to calculate the hypotenuse,altitude and base of right angle triangle.But I think that Hero's formula is also applicable in these cases.

ReplyDeleteProduct Rule

Yes, I remember the product rule used in Calculus. Very interesting approach and thanks for the reply!

ReplyDelete