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Ex 6.5, 6 - ABC is an equilateral triangle of side 2a. - Pythagoras Theoram - Finding value

  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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Ex 6.5,6 ABC is an equilateral triangle of side 2a. Find each of its altitudes. Given: Equilateral triangle ABC with each side 2a Altitude AD is drawn such that AD ⊥BC To find: AD Solution: In ∆ ADB and ∆ ADC AB = AC AD = AD ∠ ADB=∠ ADC Hence ∆ ADB ≅ ∆ ADC Hence , BD = DC BD = DC BD = DC = 1/2BC BD = DC = 2𝑎/2 BD = DC = a Hence BD = a Hence in right ∆ 𝐴𝐷𝐵 Using Pythagoras theorem (Hypotenuse)2 = (Height )2 + (Base)2 (AB)2 = (AD)2 + (BD)2 (2a)2 = (AD)2 + a2 4a2 = (AD)2 + a2 4a2 – a2 = AD2 3a2 = AD2 AD2 = 3a2 AD = √3 a AD = a√3 Thus, length of altitude AD = a√3 Similarly , length of altitude BE = a√3 length of altitude CF = a√3

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