In triangle ABC, \(\angle A = 30^\circ\), \(\angle B = 60^\circ\) and \(\angle C = 90^\circ\). In triangle DEF, \(\angle D = 30^\circ\), \(\angle E = 60^\circ\) and \(\angle F = 90^\circ\). If \(AB:DE = 2:3\), what is the ratio of the areas of the two triangles?
4:9
Both triangles have identical angles \(30^\circ, 60^\circ, 90^\circ\), so by AAA they are similar.
For similar triangles, ratio of areas equals the square of the ratio of corresponding sides.
Given \(AB:DE = 2:3\), the area ratio is \(2^2 : 3^2 = 4:9\).
Hence, the ratio of the areas of the two triangles is 4:9.
Similar Questions
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Important Questions from Triangles, Congruence and Similarity
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If the ratio of corresponding sides of 2 similar triangles is 2 ∶ 3. Then the ratio of their corresponding altitude is :
