. In ΔABC, points D and E lie on sides, AB and AC such that DE||BC and AD = 8 cm, AB = 12cm, AE = 12cm, then the length of CE is.
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. In ΔABC, points D and E lie on sides, AB and AC such that DE||BC and AD = 8 cm, AB = 12cm, AE = 12cm, then the length of CE is.
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Verified answer
CE=6 cm
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Answer:
Basic Proportionality Theorem (Thales Theorem)
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=8 cm, AB=12 cm and AE=12 cm.
Using the basic proportionality theorem, we have
AD/AB = AE/AC = DE/BC
⇒AD/AB = AE/AC
⇒8/12 = 12/AC
= 8AC = 12 × 12
⇒8AC=12×12
⇒8AC=144
⇒AC=144/8
=18
Now, CE=AC−AE=18−12=6 cm
Hence, CE=6 cm.
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