If you have 3 yards of trim to put around a rectangular scarf and you want the width of the scarf to be between 6 and 12 inches. If you want to use all the trim, what are the possible dimensions of the scarf in inches?
45 * 9
Can you find other combinations?
To find the possible dimensions of the scarf, we need to use the given information:
1. We have 3 yards of trim to put around the scarf. Since there are 3 feet in a yard, we have a total of 9 feet of trim (3 yards x 3 feet/yard = 9 feet).
2. The trim will go around the entire perimeter of the scarf. Therefore, the length of the scarf will be equal to the perimeter of the rectangle.
Now, let's calculate the perimeter of the rectangle:
Perimeter = 2 × (length + width)
Since we want to use all the trim, the perimeter should equal 9 feet.
Let's substitute the values and solve for the dimensions of the scarf:
9 = 2 × (length + width)
Dividing both sides of the equation by 2, we get:
4.5 = length + width
Now, we need to consider the second given condition: the width should be between 6 and 12 inches. Let's substitute the value of width and solve for the length:
6 ≤ width ≤ 12
Substituting the value of width in the equation:
4.5 = length + width
4.5 = length + 6 (minimum width)
Subtracting 6 from both sides, we get:
4.5 - 6 = length
-1.5 = length
Therefore, when the width is 6 inches, the length would be -1.5 inches, which is not possible, as length cannot be negative. Hence, this is not a valid solution.
Similarly, using the maximum width:
4.5 = length + 12 (maximum width)
Subtracting 12 from both sides, we get:
4.5 - 12 = length
-7.5 = length
Again, this is not a valid solution, as length cannot be negative.
Therefore, there are no valid dimensions of the scarf that satisfy the given conditions.