ICSE Class X Math 2014 Paper

In $\triangle ABC, \angle ABC = \angle DAC. AB = 8\ \mathrm{cm}, AC =$ $4\ \mathrm{cm}, A\ D=5\ \mathrm{cm}$ .

Question : 27 of 52

Marks: +1, -0

Find area of

\triangle A C D

: area of

\triangle A B C

Solution:

\because \;\; \triangle ACD \sim \triangle ABC

\therefore \;\; \frac{\text{area}(\triangle ACD)}{\text{area}(\triangle ABC)} \;=\; \frac{AC^2}{BC^2}

\;= \left(\frac{AC}{BC}\right)^2 = \left(\frac{4}{6.4}\right)^2 = \left(\frac{5}{8}\right)^2

\; \text{area}\,(\triangle ACD) \;: \text{area}(\triangle ABC)=25:64

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