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In fig triangle ABC is an …

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In fig triangle ABC is an equilateral triangle in which AD is perpendicular to BC prove that 3AD×AD = 4AD×AD

    • Posted by Aadil Raza 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago


    In equilateral {tex}\Delta ABC{/tex}, AD{tex}\perp{/tex}BC
    and AB=BC=CA 
    Also BD={tex}\frac{BC}{2}{/tex}.....(1)
    So, {tex}\Delta ABD{/tex} is right-angled triangle
    By the Pythagoras theorem,
    AB2 = AD2 + BD2
    {tex}\Rightarrow{/tex} AB2 = AD2 + ({tex}\frac{BC}{2}{/tex})2
    {tex}\Rightarrow{/tex} AB2 = AD2 + {tex}\frac{BC^2}{4}{/tex}
    {tex}\Rightarrow{/tex} 4AB2 = 4AD2 + BC2
    {tex}\Rightarrow{/tex} 4AB2 = 4AD2 + AB2 (AB = BC)
    {tex}\Rightarrow{/tex} 4AB2 = 4AD2 + AB2 
    {tex}\Rightarrow{/tex} 4AB2 - AB2 = 4AD2
    {tex}\Rightarrow{/tex} 3AB2 = 4AD2
    Hence Proved.

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