ICSE Class X Math 2014 Solved Paper

In $△ A B C, ∠ A B C=∠ D A C . A B=8 {\cm}, A C=$ $4 {\cm}, A D=5 {\cm}$ .

Question : 26 of 52

Marks: +1, -0

Find

B C

and

C D

Solution:

∵ \;\; △ {\ACD}\;∼ ∆ {\BCA}

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

⇒ \;\; \;{4}/{ {\BC}}=\;{ {\CD}}/{4}\;=\;{5}/{8}

\; ∴ \;\; \;{4}/{ {\BC}}=\;{5}/{8} \;\text " and "\; \;{ {\CD}}/{4}=\;{5}/{8}

\;⇒ \;\; {\BC}=\;{4 × 8}/{5}=\;{32}/{5}=6.4 {\cm} .

and

{\CD}=\;{5}/{8} × 4=\;{5}/{2}=2.5 {\cm} .

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