# In the given figure, DE || BD. Determine AC and AE.

Question:

In the given figure, DE || BD. Determine AC and AE.

Solution:

Given, $D E \| C B$.

In $\triangle A B C$ and $\triangle A D E$

$\angle A D E=\angle C \quad$ (Corresponding angles)

$\angle A=\angle A \quad$ (Common)

$\triangle A B C \sim \triangle A D E \quad$ (A.A Similarity)

$\frac{A E}{4}=\frac{12}{15}=\frac{14}{A C}$

$\frac{A E}{4}=\frac{12}{15}$

$A E \times 15=12 \times 4$

$4 E=\frac{12 \times 4}{15}$

$A E=\frac{4 \times 4}{5}$

$A E=\frac{16}{5}$

$\frac{A E}{4}=\frac{12}{15}=\frac{14}{A C}$

$\frac{12}{15}=\frac{14}{A C}$

$12 \times A C=14 \times 15$

$A C=\frac{14 \times 15}{12}$

$A C=\frac{35}{2}$

Hence the value of $A C$ and $A E$ is $\frac{35}{2}$ and $\frac{16}{5}$