Question

the lengths of diagonals PR and QS of a rhombus is 20 cm and 48 cm.Find the side of rhombus and its perimeter​

Answer 1

Given :-

• One Diagonal = 20cm
• Second Diagonal = 48cm

To Find :-

• Side of Rhombus
• Perimeter of Rhombus

Solution :-

★ Side of Rhombus ★

$\longrightarrow \sf{\sf{Side \: of \: Rhombus \: = \: \dfrac{1}{2}\: \sqrt{(diagonal1)^{2} \: + \: (diagonal2})^{2} }}\\ \\ \longrightarrow \sf{\sf{Side \: of \: Rhombus \: = \: \dfrac{1}{2}\: \sqrt{(20)^{2} \: + \:(48) ^{2} } }}\\ \\ \longrightarrow \sf{\sf{Side \: of \: Rhombus \: = \: \dfrac{1}{2}\: \sqrt{400 \: + \: 2304 } }}\\ \\ \longrightarrow \sf{\sf{Side \: of \: Rhombus \: = \: \dfrac{1}{2}\: \sqrt{2704 } }}\\ \\ \longrightarrow \sf{\sf{Side \: of \: Rhombus \: = \: \dfrac{1}{ \cancel2}\: \times \: \cancel{52 } }}\\ \\ \longrightarrow \sf{\bf{Side \: of \: Rhombus \: = \: 26cm }}$

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★ Perimeter of Rhombus ★

$\longmapsto \sf{\sf{ Perimeter \: of \: Rhombus \: = \: 4 \: \times \: Side }}\\ \longmapsto \sf{\sf{ Perimeter \: of \: Rhombus \: = \: 4 \: \times \: 26 }}\\ \longmapsto \sf{\bf{ Perimeter \: of \: Rhombus \: = \: 104cm }}$

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$\begin{gathered}\begin{gathered}\therefore\: \sf{ Side \: of \: Rhombus \: = \underline {\underline{ 26cm}}}\\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered} \therefore\: \sf{ Perimeter \: of \: Rhombus \: = \underline {\underline{ 104cm}}}\\\end{gathered}\end{gathered}$

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Formulas Related to Rhombus :-

• Side of Rhombus = ½ √d² + d²
• Perimeter = 4 × Side
• Area = ½ × product of Diagonal

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Answer 2

Answer:

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