Final answer:
The area of the rectangular sign is 45 square inches.
Step-by-step explanation:
To find the area of the rectangular sign, we need to know the length and width of the sign. Let's assume the width of the sign is 'w' inches. According to the problem, the length of the sign is 5 times its width, so the length would be 5w inches.
The perimeter of a rectangle is equal to the sum of all its sides. In this case, the perimeter of the sign is given as 36 inches. The formula for perimeter is: P = 2(length + width). Substituting the values, we get:
36 = 2(5w + w)
36 = 12w
w = 3
Substituting the value of 'w' back into the length equation, we get:
length = 5w = 5(3) = 15
Now we have the length and width of the sign. To find the area, we multiply the length and width: Area = length × width = 15 × 3 = 45 square inches.