Question

if a point O divides line segment AB of length 5.5cm in the ratio 2:3 then what will be the value of AO

Answer 1

Step-by-step explanation:

Explanation:

$\huge{\mathcal{\purple{A}{\green{N}{\pink{S}{\blue{W}{\purple{E}{\green{R}{\pink{!}}}}}}}}}$

Answer 2

${\large\orange {\mathbb\fcolorbox{yellow}{maroon}{■ SOLUTION:}}}$

$\blue{ \blacksquare \: \underline{ Given:}} \:$

$Point \: O \: divides \: {\overline{AB}} \: of \: length\: 5.5 \:cm\: in$ $the\: ratio \: 2:3.$

$\Longrightarrow \overline{AO} + \overline{OB} = 5.5\: cm \: —————— \: (i)$

$\Longrightarrow \overline{AO}:\overline{OB} = 2:3$

$Let \: {\overline{AO}} : {\overline{OB}} = 2k : 3k.$

$In \: eq. \: (i):$

$\therefore 2k + 3k = 5.5\: cm$

$\therefore 5k = 5.5\: cm$

$\therefore {\fbox{ k = 1.1 \: cm}}$

$\rightarrow {\overline{AO}} : {\overline{OB}} = 2k : 3k.$

$\: Substituting \: value\: of \:k :$

$\therefore {\overline{AO}} = 2k$

$\therefore {\overline{AO}} = 2(1.1 \: cm)$

$\therefore \boxed{ {\overline{AO} }= 2.2 \:cm}$

$\Longrightarrow The \: value \: of \: \overline{AO} \: is\: 2.2 \: cm.$