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In a right angle triangle ABC,AD …

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In a right angle triangle ABC,AD is perpendicular to BC,prove that AD^2=3BD^2

    • Posted by Adam Lynkyn 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago

    According to the question, {tex}\triangle ABC {/tex} is an equilateral triangle.
    In {tex}\triangle{/tex}ABD, using Pythagoras theorem,

    {tex}\Rightarrow{/tex} AB2 = AD2 + BD2
    {tex}\Rightarrow{/tex} BC2 = AD2 + BD2, (as AB = BC = CA)
    {tex}\Rightarrow{/tex} (2 BD)2 = AD2 + BD2, (perpendicular is the median in an equilateral triangle)
    {tex}\Rightarrow{/tex} 4BD2 - BD2 = AD2
    {tex}\therefore{/tex} 3BD2 = AD2

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