In △ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 2 cm, DB = 2.5 cm, AE = 3 cm, find AC
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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
ABAD=ACAE=BCDE⇒ABAD=ACAE⇒156=AC8⇒6AC=15×8⇒6AC=120⇒AC=6120=20
Hence, AC=20 cm.
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