![w\geq 14](/tex.php?f=w\geq 14)
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
![2l+2w\geq 40](/tex.php?f=2l+2w\geq 40)
we are given
length of parallelogram is 6 feet
so,
l=6
we can plug it
![2\times 6+2w\geq 40](/tex.php?f=2\times 6+2w\geq 40)
now, we can solve for w
![12+2w\geq 40](/tex.php?f=12+2w\geq 40)
subtract both sides by 12
![12+2w-12\geq 40-12](/tex.php?f=12+2w-12\geq 40-12)
![2w\geq 28](/tex.php?f=2w\geq 28)
divide both sides by 2
and we get
![w\geq 14](/tex.php?f=w\geq 14)
so,
the smallest possible measurement of the width is 14 feet