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a picture is to be mounted on a board. show that the picture and the board are not mathematically similar

a picture is to be mounted on a board. show that the picture and the board are not-example-1
User Sam Baumgarten
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1 Answer

21 votes
21 votes

Explanation:

to be similar the 2 shapes must fulfill 2 criteria :

1. they must have the same angles (since both are rectangles, this is fulfilled).

2. all pairs of corresponding sides must have the same scaling factor.

if the 8cm picture and the 10cm board sides are corresponding sides, then the scaling factor e.g. from the board to the picture is 8/10 = 4/5.

now, the other sides must follow the same factor.

but there we have 10cm (picture) and 12cm (board), and that is a factor from board to picture of 10/12 = 5/6.

but 4/5 is NOT equal to 5/6.

so, this criteria is not fulfilled.

to be safe, let's check if maybe the the sides should be paired differently.

so, 8cm (picture) to 12cm (board). that factor board to picture is 8/12 = 2/3.

and the other side pair is then 10cm to 10cm and that factor is 10/10 = 1/1.

and 2/3 is NOT equal to 1/1.

so, definitely, the second criteria is not fulfilled (no matter how we look at it).

therefore, the 2 shapes are not similar.

User Rohit Nigam
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