Given two similar triangles ABC and PQR. If their corresponding altitudes AD and PS are in the ratio 5 : 11, then the ratio of the areas of ABC and PQR is
Question
Given two similar triangles ABC and PQR. If their corresponding altitudes AD and PS are in the ratio 5 : 11, then the ratio of the areas of ABC and PQR is
Solution
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding lengths. In this case, the corresponding lengths are the altitudes of the triangles.
Given that the ratio of the altitudes AD and PS is 5 : 11, the ratio of the areas of triangles ABC and PQR will be (5/11)^2 = 25 : 121.
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