Question

which set represents a Pythagorean triple?
1,2,3
9,12,16
30,40,50
38,44,49

Answer 1

If the sides a, b, c satisfy
\(\color{#000000 }{ \displaystyle a^2+b^2=c^2 }\)

then that is a pythegorean triple

Answer 2

so A?

Answer 3

1²+2²=3²
1+4=9

I doubt that...

Answer 4

(next time please show the work)

Answer 5

okay. thank you

Answer 6

As Solomon said a Pythagorean triple is one that this equation is correct for the lengths of its sides:
\[a^{2}+b^{2}=c^{2}\]

You must see this equation like this:
\[a^{2}+b^{2}=(longest side length)^{2}\]

so in choice one, we can check it this way --> longest side=3
\[c^{2}=9\]
now if the sum of other two lengths squared equals 9, it is a Pythagorean triple. Let's Check:
\[1^{2}+2^{2}=1\times1+2\times2=1+4=5\]
But 5 is not equal to 9. SO--> It's NOT a Pythagorean triple.

Let's check choice B:
9,12,16 --> The longest side=16
\[c^{2}=16^{2}=256\]
Let's substitute the two shorter sides in the equation and check:
\[9^{2}+12^{2}=9\times9+12\times12=81+144=325\]
But 325 is not equal to 256. SO it's NOT the correct choice.

Test other two left choices and give me the answer.

Do Great!

Answer 7

By the way, when you're calculating other choice, big numbers might make it difficult to do calculation.
To make things easier, reduce the lengths of all three sides to smaller numbers if you can.
For example in choice C, you know that 30,40 and 50 can be divided by 10. So don't wait to lose your time, divide ALL THE LENGTHS by 10. It will give you 3,4,5. Now check these numbers. If 3,4,5 make a pythagorean triple, certainly 30,40 and 50 will make a pythagorean triple too.