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Question 1176153: Thank You for your help. My question is about proportional reasoning: A photo which measures 3/5 inches is enlarged to 200% what is the ratio and proportion between the original and the enlarged picture. is the square of the original picture more square than the blown up image or stays the same?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if the increase is 200%, then all dimensions of the original photo will be 2 times as large as they once were, except for the area.
that will be 2^2 = 4 times as large,
however, the square root of the area will be 2 times as large.
for example:
the picture is 3 by 4.
the area would be 3 * 4 = 12
th4e diagonal would be sqrt(3^2 + 4^2) = sqrt(25) = 5
you enlarge the photo by 200%.
the new picture is 6 by 8.
the new area would be 6 * 8 = 48.
the new diagonal would be sqrt(6^2 + 8^2) = sqrt(100) = 10
the length and the width and the diagonal were increased by a factor of 2.
the are was increased by a factor of 2^2 = 4.
howevver, the square root of the area was increased by a factor of sqrt(4) = 2, same as the dimensions.
this is the same concept of similar triangle you may have leaned in geometry, and of similar polygons you may also have leaned.
here's a reference.
https://mathbitsnotebook.com/Geometry/Similarity/SMArea.html#:~:text=If%20two%20polygons%20are%20similar%2C%20the%20ratio%20of%20their%20areas,surface%20%22area%22%20measurement.)
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