The ratio of the total surface areas of two similar prisms is 49 : 64. What is the ratio of their sides?

Step-by-step explanation:

Area is a squared measure whereas perimeter is a one-to-one measure.  Perimeter measure is also the same thing as "the ratio of the sides".  So get from the ratio of the sides to the ratio of the area, you square the one-to-one, since area is a squared measure.  You do the same to go backwards from area to one-to-one (take the square root).  

Since we are given the ratio of the areas, those numbers are the one-to-one measures squared.  Take the square root of each to find the one-to-one:

7:8 is the ratio of the sides.

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step-by-step explanation: