two isosceles triangles whose vertical angles are equal are placed so as to have their vertices coincide. prove that the line joining their

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two isosceles triangles whose vertical angles are equal are placed so as to have their vertices coincide. prove that the line joining their angular points are equal

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Natalia 1 month 2021-09-16T16:46:29+00:00 1 Answer 1 views 0

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    2021-09-16T16:48:00+00:00

    MATHS

    In given figure two isosceles triangles have equal vertical angles and their areas are in the ratio 16:25. Find the ratio of their corresponding heights.

    question

    November 22, 2019

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    Debabrata Sevda

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    ANSWER

    Let △ABC and △DEF be the given triangles such that AB=AC and DE=DF, ∠A=∠D

    and

    Area(△DEF)

    Area(△ABC)

    =

    25

    16

    …….(i)

    Draw AL⊥BC and DM⊥EF.

    Now, AB=AC,DE=DF

    AC

    AB

    =1 and

    DF

    DE

    =1

    AC

    AB

    =

    DF

    DE

    DE

    AB

    =

    DF

    AC

    Thus, in triangles ABC and DEF, we have

    DE

    AB

    =

    DF

    AC

    and ∠A=∠D [Given]

    So, by SAS-similarity criterion, we have

    △ABC∼△DEF

    Area(△DEF)

    Area(△ABC)

    =

    DM

    2

    AL

    2

    25

    16

    =

    DM

    2

    AL

    2

    [Using (i)]

    DM

    AL

    =

    5

    4

    Hence, AL:DM=4:5…..

    ……i hope it’s helpful for u……

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