the length of a rectangular jewlery box is 6 inches more than twice the width. the perimeter is 36 inches. find the length and width?
L=2W+6
Perimeeter=2W+2L=2*(W+L)=2*(W+2W+6) =2*(3W+6)=6W+12
Perimeter is 36 inches
6W+12=36 , 6w=36-12=24 Divided with 6
W=(24/6)=4 W=4
L=2W+6=2*4+6=8+6=14 L=14
Perimeter 2*(L+W)=2*(4+14)= 2*18= 36in
To find the length and width of the rectangular jewelry box, we can set up two equations based on the given information.
Let's assume the width of the jewelry box is "w" inches.
According to the problem, the length of the jewelry box is 6 inches more than twice the width. So, the length can be represented as (2w + 6) inches.
Now, we can set up the equation for the perimeter of the jewelry box, which is the sum of all four sides:
Perimeter = 2(length + width)
36 = 2((2w + 6) + w)
Now, let's simplify and solve the equation to find the value of "w" (width):
36 = 2(3w + 6)
Divide both sides by 2:
18 = 3w + 6
Subtract 6 from both sides:
12 = 3w
Divide both sides by 3:
w = 4
So, the width of the jewelry box is 4 inches.
To find the length, we can substitute the value of "w" back into the equation for the length:
Length = 2w + 6
Length = 2(4) + 6
Length = 8 + 6
Length = 14
Therefore, the length of the rectangular jewelry box is 14 inches, and the width is 4 inches.