In the given figure, $D E \| B C$ and all measurements are given in centimetres. The length of AE i

Question

In the given figure, $D E \| B C$ and all measurements are given in centimetres. The length  of AE is  \

Professor PC Thomas Classes · Answer

(b): In $	riangle A B C$, we have, $D E \| B C$\ $	herefore \quad \frac{A D}{B D}=\frac{A E}{C E}$\ (By B.P.T.)\ $\Rightarrow \frac{3}{4}=\frac{A E}{3} \Rightarrow A E=\frac{3 	imes 3}{4}=\frac{9}{4}=2.25$\ $	herefore \quad$ The length of $A E$ is 2.25 cm . \Alternative method - In $	riangle A B C$, we have, $D E \| B C$ \ By basic proportionality theorem, we have\ $\frac{A D}{A B}=\frac{A E}{A C}$\ $\Rightarrow \frac{3}{4+3}=\frac{x}{x+3}$, where $A E=x \mathrm{~cm}$\ $\Rightarrow \frac{3}{7}=\frac{x}{x+3} \Rightarrow 3(x+3)=7 x$\ $\Rightarrow 3 x+9=7 x \Rightarrow 9=4 x \Rightarrow x=9 / 4=2.25 \mathrm{~cm}$\