If two similar triangles have a linear scale factor 1:3, what is the ratio of their areas?

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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 a linear scale factor 1:3, what is the ratio of their areas?

Explanation:
When figures are similar, their linear measurements scale by the same factor, and their areas scale by the square of that factor. Here the linear scale factor is 1 to 3, so the lengths of the larger triangle are three times those of the smaller one. Since area grows with length squared, the area ratio is 1^2 to 3^2, which is 1:9. So the smaller triangle has one ninth the area of the larger.

When figures are similar, their linear measurements scale by the same factor, and their areas scale by the square of that factor. Here the linear scale factor is 1 to 3, so the lengths of the larger triangle are three times those of the smaller one. Since area grows with length squared, the area ratio is 1^2 to 3^2, which is 1:9. So the smaller triangle has one ninth the area of the larger.

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