Share
Let a and b be the leg lengths of a right triangle, and let c be the length of the hypotenuse. If all three are natural numbers, and a is an
Question
Let a and b be the leg lengths of a right triangle, and let c be the length of the hypotenuse. If all three are natural numbers, and a is an odd prime number, prove that the number 2(a+b+1) is a square of some natural number.
in progress
0
Mathematics
3 years
2021-07-30T23:46:39+00:00
2021-07-30T23:46:39+00:00 1 Answers
14 views
0
Answers ( )
Answer:
this has been proven to be true
Step-by-step explanation:
from pythagoras theorem, we know that for any right angkd triangle
a²+b² = c²
if a is an odd number as well as a prime number,
a= 3
b = 4
such that
2(a+b+1) = 2(3+4+1) = 2 * 8 = 16
16 is a square of 4.
also if a = 5 and b = 2
2(5+2+1) = 2*8 = 16
16 is a square of 4
so this has been proven to be true for the odd and prime numbers of a.