Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD). The perimeter of a rectangular traffic sign is 106 inches. Also, its length is 11 inches longer than its width. Find the dimensions of this sign.
L = W + 11
2L + 2W = 106
Substitute W+11 for L in the second equation and solve for W. Insert that value into the first equation to solve for L. Check by putting both values into the second equation.
To find the dimensions of the traffic sign, we can set up a system of equations based on the given information.
Let's start by assigning variables to the dimensions of the sign. Let's say the width of the sign is 'w' inches.
According to the given information, the length of the sign is 11 inches longer than its width, so we can express the length as 'w + 11' inches.
The perimeter of a rectangle is calculated by adding all four sides together. In this case, the perimeter is given as 106 inches, so we can write the equation:
2w + 2(w + 11) = 106
Simplifying the equation:
2w + 2w + 22 = 106
4w + 22 = 106
Now, we can solve for 'w':
4w = 106 - 22
4w = 84
Dividing both sides by 4:
w = 84/4
w = 21
So, the width of the sign is 21 inches.
To find the length, we can substitute the value of 'w' into the equation we created earlier:
Length = w + 11
Length = 21 + 11
Length = 32
Therefore, the dimensions of the traffic sign are 21 inches (width) and 32 inches (length).