Apply scale factors to length, area, and volume using k, k^2, and k^3 relationships.
Find the linear scale factor from an area ratio
Problem
Given the area ratio \(\text{image}:\text{original}~=~9:1\), find the linear scale factor.
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What this problem is really about
The given comparison is two-dimensional, but the requested factor is linear, so the area relationship must be reversed. We’ll preserve the image-to-original ratio, set it equal to the square of the length factor, take the positive square root, and verify by squaring the recovered factor.
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