the length of a rectangular road sign is 3 feet more than 2 times its width. Find the dimensions if the perimeter is 30 feet
P = 2L + 2W
30 = 2(2W + 3) + 2W
30 = 6W + 6
24 = 6W
4 = W
To find the dimensions of the rectangular road sign, we need to assign variables to the width and length. Let's say the width is represented by "w" feet.
The problem states that the length of the sign is 3 feet more than 2 times its width. So, the length can be represented as 2w + 3 feet.
The perimeter of a rectangle is given by the formula: P = 2(length + width). In this case, the perimeter is stated as 30 feet. We can substitute the given values into the formula to form an equation:
30 = 2((2w + 3) + w)
Next, we simplify the equation:
30 = 2(3w + 3)
30 = 6w + 6
6w = 30 - 6
6w = 24
w = 24/6
w = 4
Now we have found the value of the width, which is 4 feet. We can substitute this value back into the equation for the length:
Length = 2w + 3
Length = 2(4) + 3
Length = 8 + 3
Length = 11
Therefore, the dimensions of the rectangular road sign are:
Width = 4 feet
Length = 11 feet