Question 11 Mark

In the following figure $\Delta ABC$, $B-D-C$ and $BD=7$, $BC=20$, then find $\frac{A(\Delta ABD)}{A(\Delta ABC)}$.

Answer

$\Delta ABD$ and $\Delta ABC$ have a common vertex A and their bases BD and BC lie on the same line. Therefore, they have the same height.
The ratio of areas of triangles with equal heights is equal to the ratio of their corresponding bases.
$\frac{A(\Delta ABD)}{A(\Delta ABC)} = \frac{BD}{BC}$
Given $BD = 7$ and $BC = 20$.
$\frac{A(\Delta ABD)}{A(\Delta ABC)} = \frac{7}{20}$

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