If the sides of two similar triangles are in the ratio 2:3, what is the ratio of their areas?

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{"type":"doc","content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (State the Theorem):","type":"text"},{"text":" The Area Similarity Theorem states that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.","type":"text"}],"type":"paragraph"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Direct Calculation):","type":"text"},{"text":" We are given that the sides are in the ratio ","type":"text"},{"attrs":{"latex":"2:3"},"type":"math_inline"},{"text":":","type":"text"}]},{"attrs":{"latex":"\text{Ratio of Areas} = \left(\text{Ratio of Sides}\right)^2"},"type":"math_block"},{"attrs":{"latex":"\text{Ratio of Areas} = \left(\frac{2}{3}\right)^2 = \frac{4}{9}"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):","type":"text"},{"text":" The ratio of their areas is exactly ","type":"text"},{"marks":[{"type":"code"}],"text":"4:9","type":"text"},{"text":" (or ","type":"text"},{"marks":[{"type":"code"}],"text":"4/9","type":"text"},{"text":").","type":"text"}],"type":"paragraph"}]}

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