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Basic Proportionality Theorem

In ABC, D...

Question

In $△ A B C$ , $D E ∥ B C$ and $A D = 6 c m, D B = 9 c m$ and $A E = 8 c m$ , then find $A C$ .

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Solution

In $△ A B C$ ,
$D E ∥ B C$
$\frac{A D}{D B} = \frac{A E}{E C}$ (by basic proportionality theorem)
$\Rightarrow$ $\frac{6}{9} = \frac{8}{C E}$
$\Rightarrow$ $6 \times C E = 9 \times 8$
$\Rightarrow$ $C E = \frac{8 \times 9}{6}$
$\Rightarrow$ $C E = 12 c m$
$A C = A E + C E$
$= (8 + 12) c m = 20 c m$
Thus, $A C = 20 c m$

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