Question

the area of a rhombus is 192 cm2.if the length of one of its diagonal is 24 CM, find the length of the other diagonal​

Answer 1

Given :

• Area of Rhombus = 192 cm²
• 1st Diagonal of Rhombus = 24 cm

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To Find :

• 2nd Diagonal of the Rhombus = ?

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Solution :

❒ Formula Used :

• ${\underline{\boxed{\purple{\sf{ Area{\small_{(Rhombus)}} = \dfrac{1}{2} \times D_1 \times D_2 }}}}}$

Where :

• ➳ ${\sf{ D_1 }}$ = 24 cm
• ➳ ${\sf{ D_2 }}$ = ?
• ➳ Area = 192 cm²

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❒ Calculating the 2nd Diagonal :

$\begin{gathered} \dashrightarrow \; \; \sf { Area = \dfrac{1}{2} \times D_1 \times D_2 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 192 = \dfrac{1}{2} \times 24 \times D_2 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 192 = \dfrac{1}{\cancel2} \times \cancel{24} \times D_2 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 192 = 1 \times 12 \times D_2 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 192 = 12 \times D_2 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \dfrac{192}{12} = D_2 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \cancel\dfrac{192}{12} = D_2 } \\ \end{gathered}$

$\begin{gathered} \; \; {\qquad \; \; {\therefore \; {\underline{\boxed{\orange{\pmb{\frak{ Diagonal \; 2 = 16 \; cm }}}}}}}} \\ \end{gathered}$

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❒ Therefore :

❛❛ 2nd Diagonal of the Rhombus is 16 cm . ❜❜

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