In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3
BC. Prove that 9 AD^2 = 7 AB^2
Answers
Answered by
1
Step-by-step explanation:
AB=BC=AC
Construction:
Draw an Altitude AE such that,
E lies on BC and
AE perpendicular to BC
In △AEB
By Pythagoras Theorem,
AB
2
=AE
2
+EB
2
(1)
In △AED
By Pythagoras Theorem,
AD
2
=AE
2
+ED.(2)
From 1) and 2)
AD
2
=ED
2
+AB
2
−EB
2
(3)
Since, EB=
2
1
BC=
2
AB
=
6
3AB
and
ED=
6
BC
=
6
AB
∴ AD
2
=
36
AB
2
+AB
2
−
36
9AB
2
∴ 9AD
2
=7AB
2
Answered by
0
Answer:
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Step-by-step explanation:
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