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Rajan@2021
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Two isosceles triangles have equal vertical angles and their areas are in the ratio 7:16. Find the ratio of their corresponding height

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A basic and conceptual question from similarity chapter in which we have been asked to find the ratio of their corresponding height if two isosceles triangles have equal vertical angles and their areas are in the ratio 7:16

ML Aggarwal Avichal Publication class 10, Similarity, chapter 13.3, Question no 16

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  1. Consider the two isosceles triangle PQR and XYZ,
    P=X … [from the question]
    So, Q+R=Y+Z
    Q=R and Y=Z [because opposite angles of equal sides]
    Therefore, Q=Y and R=Z
    PQRXYZ
    Then, area of PQR/area of XYZ=PM2/XN2 … [from corollary of theorem]
    PM2/XN2=7/16
    PM/XN=√7/√16
    PM/XN=√7/4
    Therefore, ratio of PM:DM=√7:4

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