The ratio of the surface areas of two similar solids is 16:144. What is the ratio of their corresponding side lengths?A.4:12B.4:C.:12D.1:96
Question
The ratio of the surface areas of two similar solids is 16:144. What is the ratio of their corresponding side lengths?
A. 4:12
B. 4:C.:12
C. 1:96
Solution
The ratio of the surface areas of two similar solids is the square of the ratio of their corresponding side lengths. This is because surface area is a two-dimensional measurement, and when you scale a figure, the scale factor is squared for two-dimensional measurements.
Given that the ratio of the surface areas is 16:144, we take the square root of both numbers to find the ratio of the corresponding side lengths.
The square root of 16 is 4, and the square root of 144 is 12.
Therefore, the ratio of their corresponding side lengths is 4:12, which corresponds to option A.
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