a You can choose any positive side length to draw square ABCD.
B
b Fill in the given table by using the measures from Part A.
C
c Compare the side lengths and the perimeter of the squares.
A
aExample Graph:
B
bExample Table:
ABCD
MNPQ
FGHJ
Side length
4
Side length
8
Side length
2
Perimeter
16
Perimeter
32
Perimeter
8
C
c See solution.
Practice makes perfect
a In this exercise, we will explore how changing the length of the sides of a shape by a factor changes the perimeter of that shape. In order to do this, let's draw the three squares.
ABCD
MNPQ
FGHJ
We are told that the sides of MNPQ are twice as long as ABCD and the sides of FGHJ are half as long as ABCD. While there are infinitely many side lengths that could fit these requirements, we will choose the side length of ABCD to be 4.
b Let's fill in the given table by using the measures from Part A. Remember that the perimeter of a square is 4* a where a is side length of the square.
ABCD
MNPQ
FGHJ
Side length
4
Side length
8
Side length
2
Perimeter
16
Perimeter
32
Perimeter
8
c Let's interpret the data that we have from Parts A and B.
If we change the side length of a square by a factor of 2, the perimeter of the square also changes by a factor of 2.
Similarly, when we change the side length of a square by a factor of 12, the perimeter of the square also changes by a factor of 12.
Our conjecture can then be stated as: The ratio of the perimeters of squares is equal to the ratios of the side lengths.
