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Pythagorean Triple
- Thread starter yohelpme
- Start date
D
Deleted member 4993
Guest
yohelpme said:The problem is:
If 18 and 30 are members of a Pythagorean triple, what is the third member?
A. 15
B. 24
C. 35
D. 42
I don't want someone to tell me the answer, I just need help figuring out how to do it!
First rule, if two of the numbers are even - the third number is also even.
Clue - factorize the numbers - the GCD must be a factor of the third number.
Divide the (two given) numbers by the GCD - does it look like a familiar pair of a familiar triplet???
Subhotosh Khan said:yohelpme said:The problem is:
If 18 and 30 are members of a Pythagorean triple, what is the third member?
A. 15
B. 24
C. 35
D. 42
I don't want someone to tell me the answer, I just need help figuring out how to do it!
First rule, if two of the numbers are even - the third number is also even.
Clue - factorize the numbers - the GCD must be a factor of the third number.
Divide the (two given) numbers by the GCD - does it look like a familiar pair of a familiar triplet???
Thanks for the help. The first clue helped me get rid of two answer choices, but I don't get what you mean by factorize the numbers and whats GCD?
D
Deleted member 4993
Guest
yohelpme said:Subhotosh Khan said:yohelpme said:The problem is:
If 18 and 30 are members of a Pythagorean triple, what is the third member?
A. 15
B. 24
C. 35
D. 42
I don't want someone to tell me the answer, I just need help figuring out how to do it!
First rule, if two of the numbers are even - the third number is also even.
Clue - factorize the numbers - the GCD must be a factor of the third number.
Divide the (two given) numbers by the GCD - does it look like a familiar pair of a familiar triplet???
Thanks for the help. The first clue helped me get rid of two answer choices, but I don't get what you mean by factorize the numbers and whats GCD?
GCD = Greatest Common Divisor or GCF = Greatest Common Factor
In mathematics, the greatest common divisor (gcd), also known as the greatest common denominator, greatest common factor (gcf), or highest common factor (hcf), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4.
Hello, yohelpme!
\(\displaystyle \text{For a Pythagorean triple: }\:a^2 + b^2 \:=\:c^2\)
\(\displaystyle \text{We have two cases: }\;\begin{Bmatrix}[1] & 18^2 + 30^2 \:=\:c^2 \\ & \text{or}\qquad \\ [2] & 18^2 + b^2 \:=\:30^2 \end{Bmatrix}\)
\(\displaystyle \text{Case [1]: }\;18^2 + 30^2 \:=\:1224 \;\hdots\;\text{ not a square.}\)
\(\displaystyle \text{Case [2]: }\;18^2 + b^2 \:=\:30^2 \quad\Rightarrow\quad b^2 \:=\:576\)
. . . . . . .\(\displaystyle \text{Therefore: }\:b \,=\, 24 \;\;\hdots\;\text{ Answer (B)}\)
If 18 and 30 are members of a Pythagorean triple, what is the third member?
. . (A) 15 . . (B) 24 . . (C) 35 . . (D) 42
\(\displaystyle \text{For a Pythagorean triple: }\:a^2 + b^2 \:=\:c^2\)
\(\displaystyle \text{We have two cases: }\;\begin{Bmatrix}[1] & 18^2 + 30^2 \:=\:c^2 \\ & \text{or}\qquad \\ [2] & 18^2 + b^2 \:=\:30^2 \end{Bmatrix}\)
\(\displaystyle \text{Case [1]: }\;18^2 + 30^2 \:=\:1224 \;\hdots\;\text{ not a square.}\)
\(\displaystyle \text{Case [2]: }\;18^2 + b^2 \:=\:30^2 \quad\Rightarrow\quad b^2 \:=\:576\)
. . . . . . .\(\displaystyle \text{Therefore: }\:b \,=\, 24 \;\;\hdots\;\text{ Answer (B)}\)