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Two similar polygons have areas of 20 in² and 80 in². Find the scale factor of the first polygon to the second.

Two similar polygons have areas of 20 inches squared and 80 inches squared. Find the scale factor of the first polygon to the second.

Our first polygon is 20 inches squared. Our second polygon is 80 inches squared. The ratio of the first to the second is 20 over 80. We want to know what the scale factor is, but we’re dealing with area. And that means our scale factor will be squared. So first, let’s simplify the proportion of the first to the second.

20 over 80 can be reduced to one over four. Our scale factor squared equals one-fourth. One- fourth is what we get after we take the scale factor and multiply it by itself. What number times itself would give us one-fourth? We can take the square root to find out.

What is the square root of one over four? The square root of one over the square root of four. The scale factor is then one to two. Our second polygon is twice our first polygon.

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