Sophia 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 her scarf? write your answers in inches.
http://www.jiskha.com/display.cgi?id=1394487615
I only have 3
48 by 6
47 by 7
46 by 8
is there any more plz help
:) <@:)
Yes, there are more. Just follow the pattern above.
To find the possible dimensions of the scarf, we need to determine the range of values for the width.
First, let's convert the 3 yards of trim to inches. Since there are 36 inches in a yard, 3 yards is equal to 3 * 36 = 108 inches of trim.
Next, we need to account for the fact that the trim will go around the scarf's perimeter, which includes the length and the width. Therefore, the total length of the scarf's perimeter will be 2 times the width plus 2 times the length (2w + 2l).
Since we know the trim is equal to the perimeter, we can set up the equation:
2w + 2l = 108
Now, we can simplify the equation by dividing both sides by 2:
w + l = 54
We also know that the width needs to be a whole number between 6 and 12 inches. Let's consider the possible values for w within this range:
6 ≤ w ≤ 12
Now, we can substitute the values of w into the equation w + l = 54 to find the corresponding lengths:
For w = 6:
6 + l = 54
l = 54 - 6
l = 48
For w = 7:
7 + l = 54
l = 54 - 7
l = 47
For w = 8:
8 + l = 54
l = 54 - 8
l = 46
For w = 9:
9 + l = 54
l = 54 - 9
l = 45
For w = 10:
10 + l = 54
l = 54 - 10
l = 44
For w = 11:
11 + l = 54
l = 54 - 11
l = 43
For w = 12:
12 + l = 54
l = 54 - 12
l = 42
Therefore, the possible dimensions of the scarf are:
6 inches by 48 inches,
7 inches by 47 inches,
8 inches by 46 inches,
9 inches by 45 inches,
10 inches by 44 inches,
11 inches by 43 inches, and
12 inches by 42 inches.