If two similar triangles have areas 16 and 144, what is the linear scale factor (smaller:larger)?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

If two similar triangles have areas 16 and 144, what is the linear scale factor (smaller:larger)?

Explanation:
When two triangles are similar, all linear measurements scale by the same factor, and areas scale by the square of that factor. Here the areas are 16 and 144, so the area ratio is 144/16 = 9. That means the square of the linear scale factor is 9, so the linear factor from the smaller to the larger is 3. Therefore, the smaller to larger linear scale factor is 1:3. The other options either imply the reverse orientation (larger to smaller) or produce an area ratio that doesn’t match 16 to 144.

When two triangles are similar, all linear measurements scale by the same factor, and areas scale by the square of that factor. Here the areas are 16 and 144, so the area ratio is 144/16 = 9. That means the square of the linear scale factor is 9, so the linear factor from the smaller to the larger is 3. Therefore, the smaller to larger linear scale factor is 1:3. The other options either imply the reverse orientation (larger to smaller) or produce an area ratio that doesn’t match 16 to 144.

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