if triangle ABC is an equilateral triangle such that ad perpendicular BC then ad^2= K(DC)^2 then find the value of k
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K = 3 if triangle ABC is an equilateral triangle such that ad perpendicular BC then ad²= K(DC)²
Step-by-step explanation:
ABC is an equilateral triangle
=> AB = BC = AC
AD ⊥ BC
=> ΔABD ≅ ΔACD
as AB = AC
AD = AD ( common)
∠ADB = ∠ADC = 90°
=> BD = CD = BC/2
=> BC = 2 CD
=> AC = 2CD
AD² = AC² - CD²
=>AD² = (2CD)² - CD²
=> AD² = 3CD²
K = 3
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