A Scale Drawing of a rectangular field is 10 centimeters by 8.5 centimeters. If the actual field has dimensions of 40 meters by 34 meters, which could be the scale used for the drawing?
What are your choices?
0.5
To determine the scale used for the drawing, we need to find the ratio between the dimensions of the scale drawing and the actual field.
Let's start by finding the ratio of the length dimensions:
Scale length / Actual length = 10 cm / 40 m
To compare the units, we need to convert either cm to m or m to cm.
Since the actual field measurements are in meters, we can convert the scale length to meters:
Scale length = 10 cm × (1 m / 100 cm) (converting cm to m)
= 10/100 m
= 0.1 m
Now we can calculate the length ratio:
Scale length / Actual length = 0.1 m / 40 m
= 0.1/40
= 0.0025
Similarly, let's find the ratio for the width dimensions:
Scale width / Actual width = 8.5 cm / 34 m
Converting cm to m:
Scale width = 8.5 cm × (1 m / 100 cm)
= 8.5 / 100 m
= 0.085 m
Calculating the width ratio:
Scale width / Actual width = 0.085 m / 34 m
= 0.085/34
= 0.0025
Now let's compare the two ratios:
Length ratio = 0.0025
Width ratio = 0.0025
Both ratios are equal, which means the scale used for the drawing is consistent. Therefore, the scale used for the drawing could be 1:400.