Answer:
36
Step-by-step explanation:
Width = x
Length = 4x
Perimeter = Width + Width + Length + Length (Because there are four sides; two sides are the widgth and two sides are the length)
30 (because 30 is given as the perimeter) = x + x + 4x + 4x
30 = 10x
x = 3
Width = 3
Length = 4(3) = 12
Area = Width * Length
Area = 3 * 12 = 36
The area of the rectangular sign is equal to 36 square inches, if its perimeter is 30 inches.
Given the following data:
Translating the word problem into an algebraic equation, we have;
[tex]L = 4W[/tex]
Mathematically, the perimeter of a rectangle is given by the formula;
[tex]P = 2(L+W)\\\\30 = 2(4W + W)\\\\30 = 2(5W)\\\\30 = 10W\\\\W = \frac{30}{10}[/tex]
Width, W = 3 inches
For its length:
[tex]L = 4W\\\\L = 4(3)[/tex]
Length, L = 12 inches.
Now, we can determine the area of the rectangular sign by using the formula:
[tex]Area = LW\\\\Area = 12(3)[/tex]
Area = 36 square inches.
Therefore, the area of the rectangular sign is equal to 36 square inches.
Find more information: brainly.com/question/897975
