the perimeter of a rectangular traffic sign is 120 inches Also, its length is 6 inches longer than its width
L = Length
W = Width
P = Perimeter
L = W + 6
P = 2 L + 2 W = 2 ( L + W )
120 = 2 ( W + 6 + W )
120 = 2 ( 2 W + 6 )
120 = 4 w + 12 Subract 12 to both sides
120 - 12 = 4 W
108 = 4 W Divide both sides by 4
27 = W
W = 27 in
L = W + 6
L = 27 + 6
L = 33 in
Well, this traffic sign must have some serious curves! I mean, a perimeter of 120 inches? Talk about going the extra mile! Or in this case, the extra inch.
Now let's solve this mathematical mystery. Let's call the width of the sign "W." According to the information provided, the length of the sign would be W + 6.
To find the perimeter of a rectangle, we add up all the sides. In this case, we have two lengths and two widths. So the equation becomes:
2(W + 6) + 2W = 120
Let's simplify this a bit: 2W + 12 + 2W = 120
Now, let's combine like terms: 4W + 12 = 120
Subtract 12 from both sides: 4W = 108
Finally, divide both sides by 4: W = 27
So the width of this traffic sign would be 27 inches. And because the length is 6 inches longer, the length would be 27 + 6 = 33 inches.
So there you have it, the width is 27 inches and the length is 33 inches.
To find the length and width of the traffic sign, we can set up two equations based on the given information and solve for the unknowns.
Let's let "L" represent the length of the sign and "W" represent the width.
We know that the perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
From the given information, we have two pieces of information:
1. The perimeter is 120 inches.
2. The length is 6 inches longer than the width.
Using this information, we can set up the following equations:
Equation 1: Perimeter = 2 * (Length + Width)
120 = 2 * (L + W)
Equation 2: Length = Width + 6
L = W + 6
Now we can solve these equations simultaneously.
First, let's solve equation 2 for L and then substitute it into equation 1.
L = W + 6
120 = 2 * (L + W)
120 = 2 * (W + 6 + W)
120 = 2 * (2W + 6)
120 = 4W + 12
4W = 120 - 12
4W = 108
W = 108 / 4
W = 27
Now substitute the value of W into equation 2 to find the length:
L = W + 6
L = 27 + 6
L = 33
Therefore, the width of the traffic sign is 27 inches and the length is 33 inches.
To find the perimeter of a rectangular traffic sign, we need to know the formula for finding the perimeter of a rectangle. The formula for the perimeter of a rectangle is:
Perimeter = 2 * (length + width)
Let's use this information to solve the problem:
Let's say the width of the traffic sign is 'w' inches. Since the length is 6 inches longer than the width, we can represent the length as 'w + 6' inches.
According to the problem statement, the perimeter of the traffic sign is 120 inches. So we can set up the equation:
120 = 2 * (w + w + 6)
First, we simplify the equation:
120 = 2 * (2w + 6)
Next, we distribute the 2 on the right side of the equation:
120 = 4w + 12
Now, we isolate the variable by moving the constant to the other side:
120 - 12 = 4w
108 = 4w
Finally, we solve for 'w' by dividing both sides by 4:
w = 108 / 4
w = 27
So, the width of the traffic sign is 27 inches. Since the length is 6 inches longer, the length is:
27 + 6 = 33 inches
Therefore, the width of the traffic sign is 27 inches and the length is 33 inches.