In fig. BD =8, BC =12, B - D - C, then A ( ABC ) A ( ABD ) = ? - Vidyadip

MCQ

In fig. $BD =8, BC =12, B - D - C$, then $\frac{ A (\triangle ABC )}{ A (\Delta ABD )}=$ ?

A
$2: 3$
B
$3: 2$
C
$5: 3$
D
$3: 4$

✓

Answer

$3 : 2$

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

$\triangle A B C$ and $\triangle A B D$ have the same height. ...(Given)

The ratio of the areas of two triangles with equal heights is equal to the ratio of their corresponding bases.

$\therefore \frac{A(\triangle A B C)}{A(\triangle A B D)}=\frac{B C}{B D}$

$\therefore \frac{A(\triangle A B C)}{A(\triangle A B D)}=\frac{12}{8}$

$\therefore \frac{A(\triangle A B C)}{A(\triangle A B D)}=\frac{3}{2}$

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