Use the figure below to determine the relationship between the lengths of mr and ms

Remark

I don't know if you know anything about the sine law or not. There is no obvious relationship that I see. You can find various angles and create a ratio of the two lines, but I see nothing beyond that.

Step One: Find <MSR

<MSR = 180 - 110 from the diagram.

<MSR = 70o

Step Two: Find <SMR

Every triangle has 180 degrees

<SMR + 60 + 70 = 180

<SMR + 130 = 180

<SMR = 180 - 130

<SMR = 50o

Step 3: Use the Sine Law to express the relationship between MR and MS

MR/MS = Sin(70)/Sin(60)

MR/MS = 0.9397/0.8660 = 1.0851

MR = 1.0851 * MS

We know that angle S of triangle MSR is 180-110, since angle S and 110 degrees are supplementary (on a line)

Using the sine rule,

MR/(sin(180-110) = MS/sin(60)

MR/sin(70)=MS/sin(60)

MR*(sqrt(3)/2)/sin(70)=MS

MS=MR(sqrt(3)/2)/sin(70)

MS=0.9216MR (to 4 decimal places)

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