Respuesta :
Answer:
The area of the rectangular sign is 48 squared inches
Explanation:
Here, given the perimeter of the rectangle and the relationship between the length and width, we want to get the area of the rectangle
Let the length be represented as l with the width represented as w
From the question, we have it that the length is 3 times the width
Thus:
[tex]l\text{ = 3}\times\text{ w = 3w}[/tex]Mathematically, the perimeter can be calculated as:
[tex]P\text{ = 2(l + w)}[/tex]So, we have it that:
[tex]\begin{gathered} 32\text{ = 2(w + 3w)} \\ 8w\text{ = 32} \\ w\text{ = }\frac{32}{8} \\ w\text{ = 4 inches} \end{gathered}[/tex]Now, we can get the length
It was stated that the length is 3 times the width
we have it that:
[tex]l\text{ = 3w = 3}\times4\text{ = 12 inches}[/tex]Mathematically, the area of rectangle is the product of the width and length of the rectangle as stated below:
[tex]\begin{gathered} \text{Area = length }\times\text{ width} \\ \text{Area = 12}\times\text{ 4 = 48 squared inches} \end{gathered}[/tex]
