M<ADE = M<ABC,AD = 3.8c.m.,AE= 3.6c.m. BE-2.1c.m.,BC = 9.2c.m. DE =?
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The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.
It is given that AD=6 cm, DB=9 cm and AE=8 cm.
Using the basic proportionality theorem, we have
AB
AD
=
AC
AE
=
BC
DE
⇒
AB
AD
=
AC
AE
⇒
15
6
=
AC
8
⇒6AC=15×8
⇒6AC=120
⇒AC=
6
120
=20
Hence, AC=20 cm.
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