Two similar triangles have a linear ratio of 5:3. 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

Two similar triangles have a linear ratio of 5:3. What is the ratio of their areas?

Explanation:
When two similar shapes change size, their areas change by the square of the linear scale factor. Here the sides are in the ratio 5:3, so the areas grow as 5^2 to 3^2. That’s 25 to 9, giving the ratio of areas as 25:9. So if one triangle’s linear size is five units for every three units of the other, its area is 25 times the smaller triangle’s area, while the smaller is 9 times as large as the other’s in this squared relationship. The other options would not reflect squaring the scale factor, which is why they don’t match.

When two similar shapes change size, their areas change by the square of the linear scale factor. Here the sides are in the ratio 5:3, so the areas grow as 5^2 to 3^2. That’s 25 to 9, giving the ratio of areas as 25:9.

So if one triangle’s linear size is five units for every three units of the other, its area is 25 times the smaller triangle’s area, while the smaller is 9 times as large as the other’s in this squared relationship. The other options would not reflect squaring the scale factor, which is why they don’t match.

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