P = 2L + 2W
28 = 2(5 + 2W) + 2W
28 = 10 + 4W + 2W
28 = 10 + 6W
18 = 6W
3 = W
28 = 2(5 + 2W) + 2W
28 = 10 + 4W + 2W
28 = 10 + 6W
18 = 6W
3 = W
Let's say the width is represented by 'w' inches.
According to the problem, the length is 5 inches more than twice the width, which can be represented as: length = 2w + 5.
The perimeter of a rectangle is the sum of all sides, so we can set up an equation using the given perimeter of 28 inches:
Perimeter = 2(length + width)
Substituting the values we know, we get:
28 = 2((2w + 5) + w)
Now, we can solve for 'w':
28 = 2(3w + 5)
28 = 6w + 10
18 = 6w
w = 3
Now that we have found the width, we can substitute it back into our expression for the length:
length = 2w + 5
length = 2(3) + 5
length = 6 + 5
length = 11
Therefore, the length of the rectangular jewelry box is 11 inches, and the width is 3 inches.
Let's assume the width of the jewelry box is "x" inches. According to the problem, the length is 5 inches more than twice the width, so it can be expressed as "2x + 5" inches.
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Given that the perimeter is 28 inches, we can now write the equation as follows:
28 = 2((2x + 5) + x)
Next, we can simplify and solve the equation to find the value of "x."
28 = 2(3x + 5)
28 = 6x + 10 (using the distributive property)
6x = 28 - 10
6x = 18
x = 18/6
x = 3
So, the width of the jewelry box is 3 inches.
To find the length, we substitute the value of the width (x = 3) into the expression for the length:
Length = 2x + 5 = 2(3) + 5 = 6 + 5 = 11
Therefore, the length of the jewelry box is 11 inches and the width is 3 inches.