Question

If a 1.5cm tall girl stants at a distance of 3m, from a lamp - post and castes a shadow of 4.5m on the ground, then the height of lamp post is (A) 1.5m (B) 2m (c) 2.5m (D) 2.8m.​

Answer 1

$\bf \underline{ Let} :$

$\sf \implies AB \: be \: the \: lamp \: post.$

$\sf \implies CD \: be \: the \: girl.$

$\sf \implies DE \: be \: the \: shadow.$

$\sf \implies AD \: be \: the \: distance \: of \: girl \: from \: the \: lamp \: post.$

$\bf \underline{Thus} ,$

$\sf \implies AB = \: ?$

$\sf \implies CD = 1.5 \: metre$

$\sf \implies DE = 4.5 \: metre$

$\sf \implies AD = 3 \: metre$

$\bf \underline{So} ,$

$\sf \implies \triangle \: ABE \: and \: \triangle \: CDE \: are \: similar.$

$\sf \implies They \: form \: a \: same \: shape \: [Triangle].$

$\bf \underline{Now} ,$

$\implies \sf \: \dfrac{DE}{AD + DE} = \dfrac{CD}{AB}$

$\sf \underline{Substitute \: the \: values} ,$

$\implies \sf \: \dfrac{4.5}{3 + 4.5} = \dfrac{1.5}{h}$

$\implies \sf \: \dfrac{4.5}{7.5} = \dfrac{1.5}{h}$

$\implies \sf \: \dfrac{45}{75} = \dfrac{15}{10h}$

$\implies \sf \: \dfrac{ {}^{3} \: {\!\!\!\not4\!\!\!\not5}}{75} = \dfrac{{}^{1} \: {\!\!\!\not1\!\!\!\not5}}{10h}$

$\implies \sf \: \dfrac{3}{75} = \dfrac{1}{10h}$

$\implies \sf \: 30h = 75$

$\implies \sf \: h = \dfrac{75}{30}$

$\implies \sf \: h = 2.5 \: metre$

$\underline{ \boxed{ \pink{ \sf Hence, height \: of \: the \: lamp \: post \: is \: 2.5 \: metre. }}}$