Question

The area of a rhombus is 32 sq.cm and the length of one of the diagonal
is 8cm. Calculate the length of the other diagonal?

Answer 1

Given :

• Area of Rhombus is 32 cm² .
• Length of one diagonal is 8 cm .

To Find :

• Length of other Diagonal .

Solution :

$\longmapsto\tt{{d}_{1}=8\:cm}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rhombus=\dfrac{1}{2}\times{{d}_{1}}\times{{d}_{2}}}$

Putting Values :

$\longmapsto\tt{32=\dfrac{1}{{\not{2}}}\times{{\not{8}}}\times{{d}_{2}}}$

$\longmapsto\tt{32=4\:{d}_{2}}$

$\longmapsto\tt{{d}_{2}=\cancel\dfrac{32}{4}}$

$\longmapsto\tt\bf{{d}_{2}=8\:cm}$

So , The Length of other diagonal of the Rhombus is 8 cm .

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VERIFICATION :

$\longmapsto\tt{32=\dfrac{1}{2}\times{{d}_{1}}\times{{d}_{2}}}$

$\longmapsto\tt\boxed{32=\dfrac{1}{2}\times{8}\times{8}}$

$\longmapsto\tt{32=\cancel\dfrac{64}{2}}$

$\longmapsto\tt\bf{32=32}$

HENCE VERIFIED

Answer 2

Given :

• The area of a Rhombus is 32 cm² and length of the one of its diagonal is 8 cm.

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To Find :

• Find the length of Second diagonal.

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Solution :

~ Formula Used :

$\large{\orange{\bigstar}} \: \: \: {\color{datkblue}{\underbrace{\underline{\red{\sf{ Area{\small_{(Rhombus) }} = \dfrac{1}{2} \times D_1 \times D_2 }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━}$

~ Calculating the Second Diagonal :

${\longmapsto{\qquad{\sf{ Area{\small_{(Rhombus) }} = \dfrac{1}{2} \times D_1 \times D_2 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 32 = \dfrac{1}{2} \times 8 \times D_2 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 32 = \dfrac{1}{\cancel2} \times \cancel8 \times D_2 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 32 = 1 \times 4 \times D_2 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 32 = 4 \times D_2}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ D_2 = \cancel\dfrac{32}{4}}}}} \\ \\ \ {\qquad{\sf{ Second \: Diagonal \: of \: Rhombus \: = {\underline{\underline{\green{\sf{8 \: cm}}}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━}$

Therefore :

❝ Second Diagonal of the given Rhombus is 8 cm .❞

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✬ Verification :

$\leadsto{\sf{ \dfrac{1}{2} \times D_1 \times D_2 = 32 cm² }}$

$\leadsto{\sf{ \dfrac{1}{2} \times 8 \times 8 = 32 cm² }}$

$\leadsto{\sf{ \dfrac{1}{\cancel2} \times \cancel{64} = 32 cm² }}$

$\leadsto{\sf{ 1 \times 32 = 32 cm² }}$

$\leadsto{\sf{ 32 \: cm² = 32 \: cm² }} \\ \\ \ {\underline{\red{\sf{ LHS = RHS}}}}$

Hence, Verified.

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