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  • In the given figure, <img alt="D E \| B C\; and \;\frac{A D}{D B}=\frac{3}{5}" src="https://entrancecorner.oncodecogs.com/gif.latex?D%20E%20%5C%7C%20B%20C%5C%3B%20and%20%5C%3B%5Cfrac%7BA%20D%7

In the given figure, D E \| B C\; and \;\frac{A D}{D B}=\frac{3}{5}. If AC = 4 8. , cm, then the length of AE is

Option: 1

3.6 cm


Option: 2

1.8 cm


Option: 3

2.2 cm


Option: 4

None Of these


Answers (1)

best_answer

\begin{array}{l} \text { Let } A E=x \mathrm{~cm} . \\ \text { Then, } E C=(A C-A E)=(4.8-x) \mathrm{cm} \\ \text { Now, in } \triangle A B C, D E \| B C \text { . } \\ \therefore \quad \frac{A D}{D B}=\frac{A E}{E C} \Rightarrow \frac{3}{5}=\frac{x}{(4.8-x)} \\ \Rightarrow \quad 3(4.8-x)=5 x \Rightarrow 8 x=14.4 \\ \Rightarrow \quad x=1.8 \\ \text { Hence, } A E=1.8 \mathrm{~cm} . \end{array}

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