Question

The following sets of numbers are possible side lengths of a triangle. Which of the following sets forms a Pythagorean triple?

Answer 1

Answer:

Option B is the correct answer.

Step-by-step explanation:

A Pythagorean triple has 3 positive integers a, b, and c and the formula is given as : $a^{2}+b^{2}=c^{2}$

Now, we will check all the options whereby we will take the smallest values as a and b.

A. 18, 24, 42  

$18^{2}+24^{2}=42^{2}$

=> $324+576=1764$

=> $900\neq 1764$

This is wrong option.

B. 45, 28, 53

$45^{2}+28^{2}=53^{2}$

=> $2025+784=2809$

=> $2809=2809$

This is the correct option.

C. 15, 30, 45

$15^{2}+30^{2}=45^{2}$

=> $225+900=2025$

=> $1125\neq 2025$

This is the wrong option.

D. 33, 77, 22

$33^{2}+22^{2}=77^{2}$

=> $1089+484=5929$

=> $1573\neq 5929$

This is the wrong option.

Answer 2

A Pythagorean triple means that when you do Pythagorean theorem, a, b and c will all be integer values. The largest number will always be put in for the 'c'.
Letter B is a Pythagorean triple.
28^2 + 45^2 = 53^2
784 + 2025 ?=? 2809
2809 = 2809