ATwo quantities are proportional if they have a constant ratio or unit rate. For relationships in which this ratio is not constant, the two quantities are not proportional.
BTwo quantities are proportional if they have a constant ratio or unit rate. For relationships in which this ratio is not constant, the two quantities are not proportional.
AYes, see solution.
BNo, see solution.
Practice makes perfect
We want to check whether the side length of the given figure is proportional to its perimeter. Let's start by finding the perimeter of the figure for the side length of 1, 2, 3, and 4 units. We can organize our information in a table.
Side Length (units)
1
2
3
4
Perimeter (units)
Recall that the perimeter of a square is four times its side. Using this information, we can complete the given table.
Side Length (units)
1
2
3
4
Perimeter (units)
4(1)=4
4(2)=8
4(3)=12
4(4) =16
For each side length, we can write the relationship of the perimeter and side length as a ratio in simplest form.
Side Length (units)
1
2
3
4
Perimeter (units)
4
8
12
16
Ratio
1/4
2/8=1/4
3/12=1/4
4/16=1/4
Two quantities are proportional if they have a constant ratio or unit rate. For relationships in which this ratio is not constant, the two quantities are not proportional. In this case, each ratio can be simplified to 14, so the perimeter of the square is proportional to its side length.
We want to check whether the side length of the given figure is proportional to its area. Let's start by finding the area of the figure for the side length of 1, 2, 3, and 4 units. Let's use another table to organize our information.
For each side length, we can write the relationship of the area and side length as a ratio in simplest form.
Side Length (units)
1
2
3
4
Area (square units)
1
4
9
16
Ratio
1/1=1
2/4=1/2
3/9=1/3
4/16=1/4
Two quantities are proportional if they have a constant ratio or unit rate. For relationships in which this ratio is not constant, the two quantities are not proportional. In this case, the ratios are not the same, so the area of the square is not proportional to its side length.
