Find area of \triangle A C D : area of \triangle A B C .

ICSE Class X Math 2014 Solved Paper - Question 27

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

Question : 27 of 52

Marks: +1, -0

Find area of

△ A C D

: area of

△ A B C

Solution:

∵ \;\; △ {\ACD}\;∼ △ {\ABC}

∴ \;{{\area}(△ {\ACD})}/{{\area}(△ {\ABC})}\;=\;{ {\AC}^2}/{ {\BC}^2}

\;= (\;{ {\AC}}/{ {\BC}}) ^2= (\;{4}/{6. 4}) ^2= (\;{5}/{8}) ^2

\;\text " area "\;(△ {\ACD})\;: {\area}(△ {\ABC})=25: 64

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