Question

Sophina bought 3 yards of trim to put around a rectangular scarf. She wants the width of the scarf to be a whole number that is at least 6 inches and at most 12 inches. If she uses all the trim, what are the possibles dimensions of her scarf? Write your answer in inches.

Answer 1

1 yard = 36 inches
3 yards = 36 x 3 = 108 inches

When width = 6, 
Length = [108 - 2(6) ] ÷ 2 = 48

When width = 7, 
Length = [108 - 2(7) ] ÷ 2 = 47

When width = 8,
Length = [108 - 2(8) ] ÷ 2 = 46

When width - 9, 
Length = [108 = 2(9) ] ÷ 2 = 45

When width - 10 
Length = [108 = 2(10) ] ÷ 2 = 44

When width - 11, 
Length = [108 = 2(11) ] ÷ 2 = 43

When width - 12, 
Length = [108 = 2(12) ] ÷ 2 = 42

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Answer: The possible dimensions are (a) 6 by 48, (b) 7 by 47 ,(c) 8 by 46,  (d)9 by 45, (e) 10 by 44, (f) 11 by 43 and (g) 12 by 42.
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Answer 2

3 yards = 36*3 = 108 inches
-> total of width and length = 108/2 = 54 inches, because perimeter = 2*total of length and width.

=> length + width = 54 inches
and 6 ≤ width ≤ 12
=> all possible dimensions are:
6x48
7x47
8x46
9x45
10x44
11x43
12x42