Question

Triangle ABC has side lengths 12, 16, and 20. Do the side lengths form a Pythagorean triple? Explain.

Answer 1

Yes
A pythagorean triple is three positive integars a, b, c such that a^2+b^2=c^2. Common example is (3, 4, 5) then so is (ka, kb, kc).
In your example, you have 12, 16, 20 which would look like this:
(12)^2+(16)^2=(20)^2
but if you break down your a, b, c values and see if they are multiples of 3, 4, 5 you find:
(4*3)^2+(4*4)^2=(4*5)^2
Bc
4*3=12 or your a
4*4=16 or your b
4*5=20 or your c
and k is 4
(ka, kb, kc)
(k3, k4, k5)
(4*3, 4*4, 4*5)
(12, 16, 20)