a scale drawing of a rectangular field is 10 centimeters by 8.5 centimeters. If the actual field has a dimension of 40 meters by 34 meters which could be the scale used for the drawing?
a. 0.5cm = 16m
b. 0.5 cm = 8m
c. 0.5 cm = 4m
d. 0.5 cm =2m
I multiplied 8.5 by 10 but don't know what to do after that. I got 85
10 cm = 40 m
1 cm = 4 m
0.5 cm = _______ m
To find the scale used for the drawing, you need to calculate the ratio between the dimensions of the actual field and the dimensions of the scale drawing.
First, convert the dimension of the actual field from meters to centimeters for consistency. Since 1 meter equals 100 centimeters, the dimensions of the actual field are 4000 cm by 3400 cm.
Now, divide the length of the actual field (4000 cm) by the length of the scale drawing (10 cm):
4000 cm / 10 cm = 400
Similarly, divide the width of the actual field (3400 cm) by the width of the scale drawing (8.5 cm):
3400 cm / 8.5 cm = 400
The ratio is the same for both length and width, which means the scale remains consistent. So, the scale used for the drawing is 1 cm on the scale represents 400 cm in reality.
To check which option matches this scale, divide 400 cm by 100 (to convert it back to meters):
400 cm / 100 = 4 meters.
This means that 0.5 cm on the scale drawing represents 4 meters in reality. Therefore, the correct answer is option c: 0.5 cm = 4 m.