Concept explainers
a
To prove: The Pythagoras triple, through Pythagoras rule.
a
Explanation of Solution
Given information :
Given a right
Formula used :
Pythagoras Rule
Proof :
Pythagoras rule says
If I take, n = 3,
(3, 4, 5) is one of the Pythagoras triple which satisfies rule of Pythagoras.
It can be verified as:
b
To prove: The Pythagoras triple, through Euclid’s rule
b
Explanation of Solution
Given information :
Given a right angle with sides,
Formula used :
Euclid’s rule
Proof :
Euclid says
If I take, m = 5 and n = 3,
(1,
It can be verified as:
c
To prove: The Pythagoras triple, through rule of Plato
c
Explanation of Solution
Given information :
Given a right angle with sides,
Formula used :
Plato’s rule
Proof :
If m be any even number, then
If we take, m = 6, then
It can be verified as:
d
To prove: The Pythagoras triple, through Rule of Maseres
d
Explanation of Solution
Given information :
Given a right angle with sides
Formula used :
Rule of Maseres
Proof :
If I take, m = 5 and n = 3, we have
2mn = 2.5.3=30
For verification,
In right angle, we have
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