Selective Question

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

  1. 4

  2. ×

    4.5

  3. ×

    5

  4. ×

    3

Steven Zheng Steven Zheng posted 4 weeks ago


Answer

  1. The answer is 4


    8^2 +BD^2 = AB^2

    2^2 +BD^2 = BC^2

    \therefore AB^2- BC^2 = 8^2-2^2 = 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

Steven Zheng Steven Zheng posted 4 weeks ago

Scroll to Top