In $ riangle ABC$, $DE \parallel BC$ (as shown in the figure). If $AD = 4$ cm, $AB = 9$ cm and $AC = 13.5$ cm, then the length of $EC$ is:

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Question

In $	riangle ABC$, $DE \parallel BC$ (as shown in the figure). If $AD = 4$ cm, $AB = 9$ cm and $AC = 13.5$ cm, then the length of $EC$ is:

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Accepted Answer

Step 1: By BPT: $\frac{AD}{DB} = \frac{AE}{EC}$. $DB = 9 - 4 = 5$. $\frac{4}{5} = \frac{AE}{EC}$. Also $AE + EC = 13.5$. $AE = \frac{4}{9} 	imes 13.5 = 6$. $EC = 13.5 - 6 = 7.5$ cm.

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