AD is a median of triangle ABC. G is point on AD such that AG = 2GD A line is through G parallel to BC which interested AB and AC at M and N respectively. if AM = 4 cm then AB = ?
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Answer:
From the figure,
△AGC,△AGF,△DGC are right angled at G
Using Pythagoras theorem,
AC
2
=GC
2
+AG
2
x
2
=4n
2
+4m
2
-----------------(i)
AF
2
=FG
2
+AG
2
4=n
2
+4m
2
-----------------(ii)
DC
2
=GC
2
+DG
2
2.25=4n
2
+m
2
-----------------(iii)
Solving (ii) and (iii)
n
2
=
3
1
, m
2
=
12
11
Substitute in (i)
x
2
=4n
2
+4m
2
=
3
4(1)
+
12
4(11)
=
3
4
+
3
11
=
3
15
x
2
=5
∴x = AC = 5
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