Maharashtra BoardEnglish MediumSTD 10MathsQuestion Bank - P21 Mark
MCQ
In fig. $BD =8, BC =12, B - D - C$, then $\frac{ A (\triangle ABC )}{ A (\Delta ABD )}=$ ?
A
$2: 3$
✓
$3: 2$
C
$5: 3$
D
$3: 4$
✓
Answer
Correct option: B.
$3: 2$
$3 : 2$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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