Why the sum of
a rational number and an irrational number is
always irrational.

Because the irrational number (pi for example) plus a rational number ( the square root of four is two) would be an irrational number (5.1415926535...)  

(I CAN EXPLAIN FURTHER)

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet