In Figure-6, in an equilateral triangle ABC, AD 1 BC, BE 1 AC and CF 1 AB. Prove that 4 (AD+BE+CF%) = 9 AB,In Figure-6, in an equilateral triangle ABC, AD 1 BC, BE 1 AC and CF 1 AB. Prove that 4 (AD+BE+CF%) = 9 AB,
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Step-by-step explanation:
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Answered by
0
Step-by-step explanation:
Given AD⊥ BC
D=90˚
Proof:
Since ABC is an equilateral triangle,
AB=AC=BC
ABD is a right triangle.
According to Pythagoras theorem,
AB
2
=AD
2
+BD
2
BD=1/2BC
AB
2
=AD
2
+(1/2BC)
2
AB
2
=AD
2
+(1/2AB)
2
[∵BC=AB]
AB
2
=AD
2
+1/4AB
2
AB
2
=(4AD
2
+AB
2
)/4
4AB
2
=4AD
2
+AB
2
4AD
2
=4AB
2
–AB
2
4AD
2
=3AB
2
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