Respuesta :
Answer:
The area of the actual game room is 56 square feet.
Step-by-step explanation:
Given:
The length of the rectangle is labeled 2 inches. The width of the rectangle is labeled 4.5 inches. The scale is 1 : 30.
Now, to find the actual area of the actual game room in square feet.
Let the actual length be [tex]x.[/tex]
And let the actual width be [tex]y.[/tex]
So, as the scale is 1 : 30.
And, the length labeled is 2 inches and the width labeled is 4.5 inches.
If, 1 is equivalent to 30.
Thus, 2 is equivalent to [tex]x.[/tex]
Now, to get the actual length by using cross multiplication method:
[tex]\frac{1}{30} =\frac{2}{x}[/tex]
By cross multiplying we get:
[tex]x=60\ inches.[/tex]
Therefore, the actual length is 60 inches.
Now, to get the actual width we again use cross multiplication method:
If, 1 is equivalent to 30.
So, 4.5 is equivalent to [tex]y.[/tex]
[tex]\frac{1}{30} =\frac{4.5}{y}[/tex]
By cross multiplying we get:
[tex]y=135\ inches.[/tex]
Hence, the actual width is 135 inches.
Now, to get the area of the actual game room in square feet:
We convert the length and width of actual room in feet by using conversion factor:
12 inches = 1 feet.
60 inches = [tex]\frac{60}{12}=5\ feet.[/tex]
135 inches = [tex]\frac{135}{12}=11.25\ feet.[/tex]
Thus, the actual length of room is 5 feet and the actual width is 11.25 feet.
So, we put formula to get the actual area of the room by using formula:
[tex]Area=length\times width\\\\Area=5\times 11.25\\\\Area=56.25\ square\ feet.[/tex]
Rounding the area in to whole number is 56 square feet.
Therefore, the area of the actual game room is 56 square feet.
