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Basic Proportionality Theorem

In ABC,DE∥ ...

Question

In $△ A B C, D E ∥ B C$ , point $D$ lies $A B$ and $E$ lies on $A C$ . If $A D = 3.4 c m, A B = 10 c m, A E = 5.1 c m$ then find the value of $A C$ .

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Solution

$I n : △ A B C$ using the Thales's Theorem ("If a line is drawn parallel to one side of a triangle intersecting other two sides, then it divided the two sides in the same ratio. ")

$I n : △ A B C$
$D E | | B C$ (given)
Therefore, $\frac{A D}{A B} = \frac{A E}{A C}$
$\frac{3.4}{10} = \frac{5.1}{A C}$
$A C = \frac{10 \times 5.1}{3.4} = 15 c m$

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