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Class 10>>Maths>>Triangles>>Basic Proportionality Theorem (Thales Theorem)>>In the adjoining figure, DE || AB, AD =
Question
In the adjoining figure, DE || AB, AD = 7 cm, CD = 5 cm and BC = 18 cm. Find BE and CE.
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Solution
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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 DE∣∣AB,AD=9cm, CD=5 cm and BC=13.5 cm.
Using the basic proportionality theorem, we have
CACD=ABDE=CBCE
⇒CACD=CBCE
⇒125=18CE
⇒18×5=12CE
⇒12CE=90
⇒CE=1290=7.5
Since CE=7.5 cm, therefore,
CB=CE+EB
⇒18=7.5+EB
⇒EB=17−7.5=9.5
Hence, BE=10.5 cm and
