If two similar shapes have areas in ratio 4:9, what is the ratio of their corresponding linear dimensions (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 shapes have areas in ratio 4:9, what is the ratio of their corresponding linear dimensions (smaller:larger)?

Explanation:
When two shapes are similar, their corresponding linear dimensions change in the same ratio, and their areas change with the square of that ratio. Here the area ratio is 4:9, so the linear ratio must be the square roots: 2:3. Since we’re asked for the smaller to larger, the ratio is 2:3. A quick check: if the smaller has a linear size of 2, its area scales to 4; the larger with a linear size of 3 scales to 9, giving the area ratio 4:9, as given.

When two shapes are similar, their corresponding linear dimensions change in the same ratio, and their areas change with the square of that ratio. Here the area ratio is 4:9, so the linear ratio must be the square roots: 2:3. Since we’re asked for the smaller to larger, the ratio is 2:3. A quick check: if the smaller has a linear size of 2, its area scales to 4; the larger with a linear size of 3 scales to 9, giving the area ratio 4:9, as given.

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