In an equilateral triangle ABC, D is a point on side Bc such that 4 BD = BC. P.T 16 AD2 = 13 BC2
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Answer:
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Step-by-step explanation:
ABC is an equilateral triangle in which BD= 4
BC
Drawn AE perpendicular to BC
Since AE is perpendicular to BC then BE=EC=
2
BC
[In equilateral triangle perpendicular drawn from vertex to base bisects the base]
In △AED
AD
2
=AE
2
+DE
2
......(1)
In △AEB
AB
2
=AE
2
+BE
2
......(2)
Putting the value of AE
2
from (2) in (1), we get
AD
2
=AB
2
−BE
2
+DE
2
AD
2
=BC
2
−(
2
BC
)
2
+(BE−BD)
2
[As △ABC is an equilateral triangle]
AD
2
=BC
2
−
4
BC
2
+(
2
BC
−
4
BC
)
2
AD
2
=BC
2
−
4
BC
2
+
16
BC
2
AD
2
=
16
16BC
2
−4BC
2
+BC
2
AD
2
=
16
13BC
2
16AD
2
=13BC
2
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