Which statement is true about the following pairs of rectangles?
30cm, 60cm, and 6cm, 3cm
A) they are not similar because 6/60 does not equal 30/3.
B) they are not similar because 30/3 equals 60/6.
C) they are not similar because 3/6 does not equal 30/60.
D) they are similar because 3/6 equals 30/60.
clearly they are similar since
30 cm : 60 cm = 3 cm : 6 cm = 1 : 2
my bad - didn't see hat "not" hiding there ...
To determine whether the given pairs of rectangles are similar, we need to compare their corresponding side lengths and see if there is a constant ratio between them. Let's analyze the pairs of rectangles:
Pair 1: 30cm and 6cm
Pair 2: 60cm and 3cm
To check if the pairs are similar, we compare the ratio of the corresponding side lengths:
For pair 1: 30/6 = 5
For pair 2: 60/3 = 20
As there is no constant ratio between these two values, the rectangles in the given pairs are not similar.
Now, let's review the answer choices to find the correct statement:
A) they are not similar because 6/60 does not equal 30/3: This statement is incorrect because it compares the wrong ratios.
B) they are not similar because 30/3 equals 60/6: This statement is incorrect because it compares the correct ratios but draws the wrong conclusion.
C) they are not similar because 3/6 does not equal 30/60: This statement is incorrect because it compares the wrong ratios.
D) they are similar because 3/6 equals 30/60: This statement is correct because it correctly compares the ratios and identifies the similarity between the rectangles.
Hence, the correct statement is:
D) they are similar because 3/6 equals 30/60.