$$ △ABC $$ is right angled triangle. $$ BD⊥AC $$ , $$ AD = 8 $$ , $$ DC = 2 $$ , then find the length of $$ BD $$

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Uniteasy Admin · Accepted Answer

The answer is 4


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$$ 8^2 +BD^2 = AB^2 $$
$$ 2^2 +BD^2 = BC^2 $$

$$ 	herefore  AB^2- BC^2 = 8^2-2^2  = 60 $$
 $$ \because AB^2+ BC^2 = (8+2)^2 = 100 $$

$$ 	herefore  AB^2 = \dfrac{1}{2}	imes 160  =80, AB = 4\sqrt{5}  $$ 


$$ BC^2 =  \dfrac{1}{2}	imes 40 = 20, BC = 2\sqrt{5}  $$

$$ 	herefore  BD = \dfrac{AB\cdotp BC }{AC} = \dfrac{4	imes 2	imes 5 }{10} =4  $$

Multiple Choice Question (MCQ)

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