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

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4

×
4.5

×
5

×
3
△ABC is right angled triangle. BD⊥AC , AD = 8 , DC = 2 , then find the length of BD
4
4.5
5
3
The answer is 4
8^2 +BD^2 = AB^2
2^2 +BD^2 = BC^2
\therefore AB^2 BC^2 = 8^22^2 = 60
\because AB^2+ BC^2 = (8+2)^2 = 100
\therefore AB^2 = \dfrac{1}{2}\times 160 =80, AB = 4\sqrt{5}
BC^2 = \dfrac{1}{2}\times 40 = 20, BC = 2\sqrt{5}
\therefore BD = \dfrac{AB\cdotp BC }{AC} = \dfrac{4\times 2\times 5 }{10} =4