SOLUTION: Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k>0. 1. Are rectangle 1 and Rectangle 2 similar? Wh

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Question 1113384: Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k>0.
1. Are rectangle 1 and Rectangle 2 similar? Why or why not?
2. Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
3. Write a paragraph proof to show that the area of Rectangle 2 is k^2 times the area of Rectangle 1.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
1. They are similar because corresponding sides between the two rectangles are in the ratio k, that is L%5B2%5D+=+kL%5B1%5D+ and +W%5B2%5D+=+kW%5B1%5D+.
2. P=2L+2W for a rectangle, if one scales the sides by k, the new rectangle has perimeter +P%5Bnew%5D=2kL%2B2kW+=+k%282L%2B2W%29+=+kP+
3. A=LW, if one scales the sides by k, the new area +A%5Bnew%5D+=+%28kL%29%28kW%29+=+k%5E2%28LW%29+=+k%5E2%2AA+

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