Question

$\sf \red{ Question:}$
Three girls Reshma, Salma and Mandeep are playing a game by standing on a circle of radius 5 cm drawn in the park. Reshma throws a ball to Salma, Salma to Mandeep, Mandeep to Reshma. If the distance between Salma and Reshma, and between Salma and Mandeep is 6 cm each. What is the distance between Reshma and Mandeep?

Answer 1

$\star \; {\underline{\boxed{\pmb{\red{\sf{ \; Given \; :- }}}}}}$

$\longmapsto$ Three girls Reshma, Salma and Mandeep are playing a game by standing on a circle of radius 5 cm drawn in the park. Reshma throws a ball to Salma, Salma to Mandeep, Mandeep to Reshma. If the distance between Salma and Reshma, and between Salma and Mandeep is 6 cm each.

$\star \; {\underline{\boxed{\pmb{\color{darkblue}{\sf{ \; To \; Find \; :- }}}}}}$

$\longmapsto$ What is the distance between Reshma and Mandeep ?

$\star \; {\underline{\boxed{\pmb{\pink{\sf{ \; SolutioN \; :- }}}}}}$

$\maltese$ Let us Assume :

• Reshma = R
• Salma = S
• Mandip = M

$\maltese$ Construction :

${\twoheadrightarrow{\sf{ Draw \; OL \perp RS }}}$

$\maltese$ Calculating the Distance :

Here :-

$\begin{gathered} \dashrightarrow \; \; \sf { {OL}^{2} = {OR}^{2} - {RL}^{2} } \\ \end{gathered}$

$\begin{gathered} {\dashrightarrow \; \; \sf { {OL}^{2} = {5}^{2} - {3}^{2} }} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { {OL}^{2} = 25 - 9 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { {OL}^{2} = 16 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { OL = \sqrt{16} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; {\underline{\boxed{\pmb{\sf{ OL = 4 }}}}} \; {\orange{\bigstar}} \end{gathered}$

Now :-

Area of Triangle ORS :-

$\begin{gathered} \longmapsto \; \; \sf { Area = \dfrac{1}{2} \times LR \times OS } \\ \end{gathered}$

$\begin{gathered} \longmapsto \; \; \sf { Area = \dfrac{1}{2} \times RS \times OL } \\ \end{gathered}$

$\begin{gathered} \longmapsto \; \; \sf { Area = \dfrac{1}{2} \times 6 \times 4 } \\ \end{gathered}$

$\begin{gathered} \longmapsto \; \; \sf { Area = \dfrac{1}{2} \times 24 } \\ \end{gathered}$

$\begin{gathered} \longmapsto \; \; \sf { Area = \dfrac{1}{\cancel2} \times \cancel{24} } \\ \end{gathered}$

$\begin{gathered} \longmapsto \; {\underline{\boxed{\pmb{\sf{ Area = 12 }}}}} \; {\green{\bigstar}} \end{gathered}$

So :

$\begin{gathered} \dashrightarrow \; \; \sf { Area = \dfrac{1}{2} \times LR \times OS } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 12 = \dfrac{1}{2} \times LR \times 5 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 12 \times 2 = 1 \times LR \times 5 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 24 = LR \times 5 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \dfrac{24}{5} = LR } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \cancel\dfrac{24}{5} = LR } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; {\underline{\boxed{\pmb{\sf{ LR = 4.8 \; m }}}}} \; {\red{\bigstar}} \end{gathered}$

$\maltese$ Calculating the Distance :

$\begin{gathered} \implies \; \; \sf { RM = LR \times 2 } \\ \end{gathered}$

$\begin{gathered} \implies \; \; \sf { RM = 4.8 \times 2 } \\ \end{gathered}$

$\begin{gathered} \implies \; {\underline{\boxed{\pmb{\sf{ RM = 9.6 \; m }}}}} \; {\color{darkblue}{\bigstar}} \end{gathered}$

$\therefore \;$ Distance between Reshma and Mandeep is 9.6 m .

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