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 : 26 of 52

Marks: +1, -0

Find

B C

and

C D

Solution:

\because \;\; \triangle ACD \sim \triangle BCA

\; \frac{AC}{BC} = \frac{CD}{CA} = \frac{AD}{BA}

\Rightarrow \;\; \frac{4}{BC} = \frac{CD}{4} = \frac{5}{8}

\; \therefore \;\; \frac{4}{BC} = \frac{5}{8} \; \text{ and } \; \frac{CD}{4} = \frac{5}{8}

\; \Rightarrow \;\; BC = \frac{4 \times 8}{5} = \frac{32}{5} = 6.4 \text{ cm} .

and

CD = \frac{5}{8} \times 4 = \frac{5}{2} = 2.5 \text{ cm} .

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