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This is matter of simple geometric relationships between triangles. For triangles to be of the same proportion, what you ha e to do is change all sides by the same factor as you change any one side.

The Moon is about 3,476 km in diameter, Mars has a diameter of 6,800 km (essentially twice as big). To appear to have a diameter the same as the Moon's, Mars would have to be about twice as far away. The Moon is 384,403 km away so Mars in the "as large as the moon" case would be about twice this distance or 768,800 km away.

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Q: How would you find out how far way Mars would be from Earth if Mars appeared to be as big as the Moon?
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