If A B=6 {\cm}, D E=4 {\cm} and A C=15 {\cm} . Calculate C D .

ICSE Class X Math 2013 Solved Paper - Question 14

In the given figure, $A B$ and $D E$ are perpendicular to $B C$ .

Question : 14 of 46

Marks: +1, -0

A B=6 {\cm}, D E=4 {\cm}

and

A C=15

{\cm}

. Calculate

C D

Solution:

\;\;\text " In "\; △ {\ABC} \;\text " and "\; △ {\DEC} \;\text ", "\;

\;△ {\ABC} ∼ △ {\DEC}

\;\;\text " (proved in (i) part) "\;

\; ∴ \;\; \;{ {\AB}}/{ {\DE}}=\;{ {\AC}}/{ {\CD}}

\;\;\text " Given : "\; {\AB}=6 {\cm}, {\DE}=4 {\cm}, {\AC}=15

\; {\cm} ,

\; ∴ \;\; \;{6}/{4}=\;{15}/{ {\CD}}

\;⇒ \;\; {\CD}=\;{15 × 4}/{6}

\;⇒ \;\; C D=10 {\cm} .

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