if AB=BC=AC=a mm then AD= 270mm then find a=-------mm 243 mm 311.76 mm 234 mm 256 mm
Answers
Given : AB=BC=AC=a mm AD = 270 mm
To find : Value of a
Solution:
Assuming AD ⊥ BC
AB=BC=AC=a mm
=> Equilateral triangle
=> AD ⊥ BC is also median
=> BD = CD = BC/2 = a/2
Applying Pythagoras theorem
AB² = AD² + BD²
=> a² = 270² + (a/2)²
=> a² = 270² + a²/4
=> 3a²/4 = 270²
=> a² = 270² * 4 / 3
=> a = 270 * 2/ √3
=> a = 540/√3
=> a = 180√3
using √3 = 1.732
a = 180 * 1.732 = 311.76
a = 311.76 mm is correct answer
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