Geometry math question no guessing and show work you

Here we use midsegment rule which states that if a segment joining two midpoints of the two sides ,then it is parallel to third side and equal to half of it .

That is,

SP = 0.5 LN

3x+1=0.5(10x-6)

6x+2 = 10x-6

Subtracting 6x to both sides and adding 6 to both sides

8 = 4x

Dividing both sides by 4

x=2

Substituting x in SP, that is SP =3(2)+1 =7

2*SP = LN

2(3x+1)=(10x-6)

6x+2=10x-6

10x-6x = 2+6

8x=8

x=1

SP=3x+1 =3(1) +1 =4

SP=4

Answer is D. SP=4

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