A room is 14 feet long and 11 feet wide. If you made a scale drawing of the top view of the room using scale 1/2 inches=2 feet.
What would be the length and width of the room in your drawing.
scale :
1 ft ----> 1/4 inch
14 ft ----> 7 inches
11 ft ----> 11/4 inches or 2 3/4 inches
To determine the length and width of the room in the scale drawing, we can use the given scale of 1/2 inches = 2 feet.
First, let's find the length of the room in the drawing:
The actual length of the room is 14 feet.
So, in the scale drawing, we can use the proportion:
Actual Length / Scale Length = Actual Width / Scale Width
Substituting in the known values, we have:
14 feet / Scale Length = 11 feet / Scale Width
Since the scale is 1/2 inches = 2 feet, we can represent the scale length as x inches:
14 feet / x inches = 11 feet / (x * 2) inches
Cross-multiplying, we get:
14 * (x * 2) inches = 11 * x inches
Simplifying further, we have:
28x inches = 11x inches
Dividing both sides by 11x, we find:
28 inches = 11 inches
Hence, the length of the room in the scale drawing is 11 inches.
Similarly, we can find the width of the room in the scale drawing.
The actual width of the room is 11 feet.
Using the same proportion as before:
Actual Length / Scale Length = Actual Width / Scale Width
Substituting in the known values, we have:
14 feet / Scale Length = 11 feet / Scale Width
Since the scale is 1/2 inches = 2 feet, we can represent the scale width as y inches:
14 feet / (x * 2) inches = 11 feet / y inches
Cross-multiplying, we get:
14 * y inches = 11 * (x * 2) inches
Simplifying further, we have:
14y inches = 22x inches
Dividing both sides by 22x, we find:
y inches = (22/14) x inches
Simplifying further, we have:
y inches = (11/7) x inches
Hence, the width of the room in the scale drawing is (11/7) inches, which is approximately 1.57 inches.
To determine the length and width of the room in the scale drawing, we need to use the given scale: 1/2 inches = 2 feet.
First, let's find the length of the room in the scale drawing. We can divide the actual length of the room (14 feet) by the scale factor (2 feet) to get the length in inches:
Length (in inches) = Actual Length / Scale Factor
Length (in inches) = 14 feet / 2 feet
Length (in inches) = 7
Therefore, the length of the room in the scale drawing would be 7 inches.
Next, let's find the width of the room in the scale drawing. Using the same process, we can divide the actual width of the room (11 feet) by the scale factor (2 feet) to get the width in inches:
Width (in inches) = Actual Width / Scale Factor
Width (in inches) = 11 feet / 2 feet
Width (in inches) = 5.5
Therefore, the width of the room in the scale drawing would be 5.5 inches.