The perimeter of a traffic sign must be 128 inches. It's length is 8 inches longer than the width. find the dimensions.
set x as the width;x+8 as the length
the formula for the perimeter is 2(l+w)
2[x+(x+8)]=2(2x+8)=4x+16=128
4x+16=128
4x=112
x=28
28by36
To find the dimensions of the traffic sign, we need to set up an equation using the given information. Let's start by assigning a variable to represent the width of the traffic sign.
Let's say the width of the traffic sign is 'w' inches.
According to the given information, the length of the traffic sign is 8 inches longer than the width, which means the length is 'w + 8' inches.
The perimeter of a rectangle is given by the formula: P = 2(w + l), where P is the perimeter, w is the width, and l is the length.
In this case, the perimeter is given as 128 inches, so we can set up the equation:
128 = 2(w + w + 8)
Simplifying the equation:
128 = 2(2w + 8)
Divide both sides of the equation by 2 to solve for 'w':
128/2 = 2w + 8
64 = 2w + 8
Subtract 8 from both sides:
64 - 8 = 2w
56 = 2w
Divide both sides by 2:
56/2 = 2w/2
28 = w
So, the width of the traffic sign is 28 inches.
To find the length, we can substitute this value back into our expression for the length:
Length = Width + 8 = 28 + 8 = 36 inches.
Therefore, the dimensions of the traffic sign are:
Width = 28 inches
Length = 36 inches.