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Please help me with this +!!!

Please help me with this +!!!-example-1

1 Answer

5 votes

Answer is choice D) 7:8

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Work Shown:

The ratio of the surface areas is 686:896 which reduces to 49:64 when we divide both parts by the GCF 64.

Now apply the square root to both parts to go from 49:64 to 7:8

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Here's an example why the square root comes into play. Imagine we had two rectangles where one is 3 by 5 and the other is 6 by 10. The areas of each are 3*5 = 15 and 6*10 = 60. Notice how the ratio of the areas is 15:60 which reduces to 1:4, and then that becomes 1:2 after applying the square root. Furthermore, notice how the 6 by 10 rectangle has dimensions exactly double that of the 3 by 5 rectangle, showing the linear scale factor is 1:2.

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