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The perimeter is 600, so 2w+2l=600 where w is the width and l is the length.
Divide both sides by 2: w+l=300
The length is 20 more than the width: l=w+20
Substituting in the previous equation: w+(w+20)=300
Collecting terms: 2w+20=300
Subtract 20 from both sides: 2w=280
Divide by 2: w=140
Thus the width is 140. Substituting into the equation for length: l=140+20
The width is 140 and the length is 160
Solve the resulting quadratic equation
X-2=(1/4)*(-3-27) =-(15/2), negative
Since the width must be positive, reject the negative root and keep X_1=6 Width =6
Check 6*(15)=90. Checks OK
After putting on the buttonhole foot, you lower the foot, put in the size button you want into the button hole foot. Lower the button hole lever all the way (so machine does not blip) Then the machine automatically sets the length and width of the button hole...you can adjust the length and width manually by pushing the button on the top right hand part of the machine above the LED screen the top one is stich length the other is stich width....if you put the levers to the left it will be the smallest stich length or width...if to the right it will be the largest stich length or width the machine allows. But, really the machine automatically does this for you...so I don't see the need to do it.....but you can....BBill01