Siphons 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 possible dimensions of the scarf? Write in inches. Thanks
108 = 2L + 2W
48 by 6
47 by 7
46 by 8
Take from there
To find the possible dimensions of the scarf, we need to consider the length of the trim and the possible widths of the scarf.
Since Siphons bought 3 yards of trim, we need to convert it to inches since the width of the scarf will be in inches. There are 36 inches in 1 yard, so 3 yards would be 3 * 36 = 108 inches.
Let's assume the width of the scarf is represented by "w" inches. Since the trim is used all the way around the scarf, the total length of the trim would be twice the sum of the width and length of the scarf.
So, the total length of the trim would be 2 * (w + L) inches.
Given that Siphons uses all the trim (total length = 108 inches), we can write the equation for the total length of the trim as 2 * (w + L) = 108.
To find the possible dimensions, we need to list out the whole number values of the width (w) that satisfy the equation.
Let's start with the lowest possible value for w, which is 6 inches:
2 * (6 + L) = 108
12 + 2L = 108
2L = 108 - 12
2L = 96
L = 96 / 2
L = 48
So, if the width (w) is 6 inches, the length (L) would be 48 inches.
Now, we can move on to the next possible value for w, which is 7 inches:
2 * (7 + L) = 108
14 + 2L = 108
2L = 108 - 14
2L = 94
L = 94 / 2
L = 47
So, if the width (w) is 7 inches, the length (L) would be 47 inches.
We can continue this process until we find the possible dimensions within the given range of 6 to 12 inches for the width.
Here are the possible dimensions of the scarf:
Width (w) = 6 inches, Length (L) = 48 inches
Width (w) = 7 inches, Length (L) = 47 inches
Width (w) = 8 inches, Length (L) = 46 inches
Width (w) = 9 inches, Length (L) = 45 inches
Width (w) = 10 inches, Length (L) = 44 inches
Width (w) = 11 inches, Length (L) = 43 inches
Width (w) = 12 inches, Length (L) = 42 inches