If $D E = 4 c m, C E = 5 c m$ and $B C = 9 c m$ . Find $C D, A B$ and $A C$

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Solution

$\begin{matrix} Δ A B C a n d Δ E D C a r e s i m m i l a r t h e n, b y s i m i l a r i t y o f t r i a n g l e \Rightarrow \frac{A B}{E D} = \frac{B C}{D C} \to (i) I n Δ C D E \Rightarrow \sqrt{D E^{2} + C D^{2}} = E F \Rightarrow \sqrt{4^{2} + C D^{2}} = 5 \Rightarrow 11 + C D^{2} = 25 \Rightarrow C D^{2} = 25 - 16 \Rightarrow C D = \sqrt{9} C D = 3 c m f r o m e q u a t i o n (i) \Rightarrow \frac{A B}{4} = \frac{9}{3} A B = 12 c m a n d I n Δ A B C A B^{2} + B C^{2} = A C^{2} \Rightarrow {(2)}^{2} + 9^{2} = A C^{2} \Rightarrow \sqrt{144 + 81} = A C \sqrt{225} = A C A C = 25 c m A n s . \end{matrix}$

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In the following figure, $D E ∥ A B$ . If $A D = 7 c m, C D = 5 c m$ and $B C = 18 c m$ , find $C E$ .

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△ A B C, ∠ A B C = ∠ D A C, A B = 8 c m, A C = 4 c m, A D = 5 c m

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