the lengthnof a rectangular jewelry box is 3 inches more than twice the width. the perimeter is 30 inches. find the length and the width?
Let's denote the width of the jewelry box as "W" (in inches) and the length as "L" (in inches).
According to the given information, the length is 3 inches more than twice the width. So we can write the equation:
L = 2W + 3
The perimeter of a rectangle is given by the formula:
Perimeter = 2(L + W)
Substituting the values we have:
30 = 2(2W + 3 + W)
Simplifying the equation:
30 = 2(3W + 3)
30 = 6W + 6
Subtracting 6 from both sides:
24 = 6W
Dividing both sides by 6:
4 = W
So the width of the jewelry box is 4 inches.
Substituting this value back into our first equation:
L = 2(4) + 3
L = 8 + 3
L = 11
Therefore, the length of the jewelry box is 11 inches and the width is 4 inches.
To find the length and width of the rectangular jewelry box, we can set up a system of equations based on the given information.
Let's assume that the width of the jewelry box is represented by "W" inches.
According to the problem, the length of the box is "3 inches more than twice the width." So, we can express the length as (2W + 3) inches.
The formula for the perimeter of a rectangle is given by P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
We are given that the perimeter is 30 inches, so we can set up the equation:
30 = 2(2W + 3) + 2W
Simplifying this equation:
30 = 4W + 6 + 2W
30 = 6W + 6
Next, we subtract 6 from both sides of the equation:
30 - 6 = 6W + 6 - 6
24 = 6W
Dividing both sides by 6:
24/6 = (6W)/6
4 = W
Therefore, the width of the rectangular jewelry box is 4 inches.
Now, we can substitute the value of the width (W) into the expression for the length we found earlier:
Length = 2W + 3 = 2(4) + 3 = 8 + 3 = 11 inches.
So, the width of the jewelry box is 4 inches, and the length is 11 inches.
w = width
2w + 3 = length
P = 2w + 2L
30 = 2w + 2(2w + 3)
Solve for w, the width.
2w + 3 = length