Question

Ab=3de and area of triangle abc =144 then find area of triangle def

Answer 1

$\underline{ \underline {\bold{\pink{ \: \: The \: \: question \: \: should \: \: be \: \: as \: \: follow \: : \: \: }}}}$


$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: QUESTION \: \: \red{ \mid}}}}}}}}$


$\bold{If \: \: \triangle \: ABC\: \: is \: \: similar \: \: to \: \: \triangle \: DEF \: \: and} \\ \bold{ AB= 3DE \: \: and \: \: area \: \: of \: \: \triangle \: ABC = 144,} \\ \bold{then \: \: find \: \: the \: \:area \: \: of \: \: \triangle \: DEF.}$



$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION \: \: \red{ \mid}}}}}}}}$


$\underline{ \underline{\bold{ \: \: GIVEN \: \: \: : }}} \\ \\ \bold{In \: \: \triangle \: ABC \: \: and \: \: \triangle \: DEF} \\ \\ \bold{AB = 3DE \: \: \: - - - - - - - > (1)} \\ \\ \bold{And,} \\ \\ \bold{Ar( \triangle \: \: ABC) = 144 \: \: sq.unit \: - - - - - - > (2)}$


$\underline{ \bold{ \: \: Again \: \: \: }}$

$\bold{ \triangle \: ABC \sim \triangle \: DEF}$


$\bold{ \: \: Hence ,\: \: } \\ \\ \bold{ \frac{ \: Ar( \triangle \: ABC) \: }{ \: Ar (\triangle \: DEF) \: } = \frac{ \: AB {}^{2} \: }{ \: DE{}^{2} } \: } \\ \\ \bold{ = > \frac{144}{ \: \: Ar( \triangle \: DEF )\: \: } = \frac{(3DE){}^{2} }{(DE) {}^{2} } \: \: \: \: [From \: \: (1) \: \: and \: \: (2)]\: } \\ \\ \bold{ = > \frac{144}{Ar( \triangle \: DEF)} = \frac{9DE {}^{2} }{DE {}^{2} } } \\ \\ \bold{ = > \frac{144}{Ar \: ( \triangle \: DEF) } = \frac{9}{1} } \\ \\ \bold{ = > 9(Ar \: ( \: \triangle \: DEF)) = 1 \times1 44} \\ \\ \bold{ = > 9(Ar( \triangle \: DEF)) = 144} \\ \\ \bold{ = > Ar( \triangle \: \: DEF) = \frac{144}{9} } \\ \\ \bold{ = > Ar \: ( \triangle \: DEF)= 16}$


$\bold{Therefore} \\ \\ \\ \bold{If \: \: \triangle \: ABC \: \: is \: \: similar \: \: to \: \: \triangle \: DEF\: \: and} \\ \bold{ AB= 3DE \: \: and \: \: area \: \: of \: \: \triangle \: ABC = 144 \: \: sq.unit,} \\ \bold{ then \: \: \: \: the \: \:area \: \: of \: \: \triangle \: DEF = \underline{ \: \: 16 \: \: sq.unit \: \:} }$