The ratio of the surface areas of two similar solids is 49:100. What is the ratio of their corresponding side lengths?A.:10B.7:C.7:10D.1:24
Question
The ratio of the surface areas of two similar solids is 49:100. What is the ratio of their corresponding side lengths?
A.: 10
B.: 7
C.: 7:10
D.: 1:24
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, you square the scale factor to find the new surface area.
Given that the ratio of the surface areas is 49:100, you find the ratio of the corresponding side lengths by taking the square root of each part of the ratio.
The square root of 49 is 7, and the square root of 100 is 10.
Therefore, the ratio of their corresponding side lengths is 7:10, which corresponds to option C.
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