The length of the rectangular bookmark required to Ella is 16 minus thrice its width. If the perimeter is 20 inches, determine its length and width.
L = 16 - 3 w
L + w = 20/2 = 10
so L = 10-w
10 - w = 16 - 3 w
2 w = 6
w = 3
L = 10 - 3 = 7
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check
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16 - 9 = 7 sure enough
2(7) + 2(3) = 14 + 6 = 20 . Whew !
L = 16-3W
2(16-3W)+2W = 20
16-3W+W = 10
W = 3 in.
L = 16-3W = 16-9 = 7in.
9
To solve this problem, we can use the given information and set up two equations based on the given conditions.
Let's assume the width of the bookmark is "w" inches.
According to the question, the length of the bookmark is 16 minus thrice its width, which can be written as:
Length = 16 - 3w
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
We are given that the perimeter is 20 inches. Substituting the values, we get:
20 = 2 * (16 - 3w + w)
Simplifying the equation, we have:
20 = 32 - 2w
Rearranging the equation, we get:
2w = 32 - 20
2w = 12
Dividing both sides of the equation by 2, we find:
w = 6
Therefore, the width of the rectangle bookmark is 6 inches.
To find the length, we substitute the value of w into the equation for the length:
Length = 16 - 3w
Length = 16 - 3(6)
Length = 16 - 18
Length = -2
The length of the rectangle bookmark is -2 inches (which is not a realistic solution). This means that there is no valid solution for this problem.