<h3>
Answer: The rectangles are <u>
not</u>
similar</h3>
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Explanation:
Divide the vertical sides to get the fraction 18/7
Divide the horizontal sides to get the fraction 30/6
If the rectangles were similar, then 18/7 = 30/6 is a possibility (there's one more possibility but we'll get to it later).
If 18/7 = 30/6 were true, then we should be able to cross multiply and get another true statement. Let's find out
18/7 = 30/6
18*6 = 7*30
108 = 210
We get a false statement, which means the original equation is false.
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Now let's say we rotated the bottom rectangle so that the '7's were horizontal and the '6's were vertical. We'll divide the corresponding horizontal sides and vertical sides to get the two fractions of 30/7 and 18/6
Let's see if we have a true equation or not
30/7 = 18/6
30*6 = 7*18
180 = 126
Like before, we end up with a false equation which means the original is false.
No matter how we rotate the rectangles, we do <u>not</u> end up with similar figures.
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Here's another way to see we don't have similar rectangles. We'll form the fraction 18/30 based on dividing the vertical and horizontal sides of the upper rectangle. The lower rectangle gives us 7/6
18/30 = 7/6
18*6 = 30*7
108 = 210
This is more evidence that the rectangles aren't similar. The same will happen if we tried 18/30 = 6/7
