Question

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

A. 18, 24, 42

B. 45, 28, 53

C. 15, 30, 45

D. 33, 77, 22

Answer 1

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

Answer 2

Option B is the correct answer.

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\\eq 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\\eq 2025`

This is the wrong option.

D. 33, 77, 22

`33^(2)+22^(2)=77^(2)`

=>
`1089+484=5929`

=>
`1573\\eq 5929`

This is the wrong option.