Question

Ashley claims that the sum of four multiples of 6 will be a multiple of 12. Is Ashley's conjecture reasonable? If not provide a counter-example.

Prove that the perimeter will be even for any rectangle with natural number side lengths.

Answer 1

False!
Counter-example

4 possible multiples of 6 are
6, 12, 30, and 42
their sum is 90
but 90 is not divisible evenly be 12, so the statement is false

Answer 2

for the perimeter, since
p = 2(length+width)
p is even, since it is a multiple of 2.