In fig, seg DE || sec BC, identify the correct statement.

MCQ

A
$\frac{A D}{D B}=\frac{A E}{A C}$
B
$\frac{A D}{D B}=\frac{A B}{A C}$
C
$\frac{A D}{D B}=\frac{E C}{A C}$
D
$\frac{A D}{D B}=\frac{A E}{E C}$

✓

Answer

3: 5
Let $\triangle ABC$ and $\triangle PQR$ be two similar triangles.
According to the given condition,
$
\frac{ A (\Delta ABC )}{ A (\Delta PQR )}=\frac{9}{25}
$
But $\frac{ A (\Delta ABC )}{ A (\Delta PQR )}=\frac{ AB ^2}{ PQ ^2}$
...(By the theorem of areas of similar triangles)
$
\therefore \frac{ AB ^2}{ PQ ^2}=\frac{9}{25}
$
$
\therefore \frac{ AB }{ PQ }=\frac{3}{5}
$
$\therefore 3: 5$ is the ratio of their corresponding sides.

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