A picture is 42 cm by 36 cm. A scale diagram of the picture must fit in a space that is 3 m by 2 m. Write a reasonable scale for the scale diagram.
Wow, a scale that increases...
first, which measurement will limit the scale?
300cm/42cm=7.14
200cm/36cm=5.55
so a scale of 5.5:1 will work, but honestly, most folks would scale it at 5:1
scale dimensions: 42*5=2.10m
36*5=1.8m
To find a reasonable scale for the scale diagram, we need to determine the ratio between the actual size of the picture and the size it will be represented in the scale diagram.
First, let's convert the measurements to the same unit. Since the space is given in meters, we should convert the measurements of the picture to meters as well.
The length of the picture is 42 cm, which is 0.42 meters (1 meter = 100 cm).
The width of the picture is 36 cm, which is 0.36 meters.
Now, we can compare the actual size of the picture to the representation in the scale diagram.
The space for the scale diagram is 3 m by 2 m, which gives us a ratio of 3:2.
To determine the reasonable scale for the scale diagram, we divide the actual size of the picture by the size it will be represented in the scale diagram.
For the length of the picture:
0.42 meters / 3 meters = 0.14
For the width of the picture:
0.36 meters / 2 meters = 0.18
So, a reasonable scale for the scale diagram would be 1:0.14 (or 1:14) for the length and 1:0.18 (or 1:18) for the width of the picture.