Question

of of a rhombus having side If the area of a rhombus be 48 cm² and one of its diagonal be 8 cm. Find the length diagonal.
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Answer 1

Answer:

• Length of another diagonal is 12 cm .

Step-by-step explanation:

According to the Question

It is given that,

• Area of Rhombus = 48cm²
• Length of one diagonal ,d1 = 8cm

we have to calculate the length of another diagonal .

Let , the another diagonal of Rhombus be d2 .

As we know that

• Area of Rhombus = 1/2 × d1 × d2

by putting the value we get

⇢ 48 = 1/2 × 8 × d2

⇢ 48 = 4 × d2

⇢ d2 = 48/4

⇢ d2 = 12 cm

• Hence, the length of another diagonal is 12 cm.

Answer 2

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

• Area of Rhombus = 48 cm²
• Diagonal 1 = 8 cm

$\star \: {\underline{\boxed{\pmb{\purple{\sf{ \: To \: Find \: :- }}}}}}$

• Diagonal 2 = ?

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

$\bigstar$ Formula Used :

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

Where :

• ${\sf{ D_1 = Diagonal \: 1 }}$
• ${\sf{ D_2 = Diagonal \: 2 }}$

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$\bigstar$ Calculating the 2nd Diagonal :

${\longmapsto{\qquad{\sf{ Area = \dfrac{1}{2} \times D_1 \times D_2 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 48 = \dfrac{1}{2} \times 8 \times D_2 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 48 = \dfrac{1}{\cancel2} \times \cancel8 \times D_2 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 48 = 1 \times 4 \times D_2 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 48 = 4 \times D_2 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \dfrac{48}{4} = D_2 }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \cancel\dfrac{48}{4} = D_2 }}}} \\ \\ \\ \ {\qquad \: \: {\therefore \: {\underline{\boxed{\pmb{\red{\frak{ Diagonal \: 2 = 12 \: cm }}}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

$\bigstar$ Therefore :

❛❛ 2nd Diagonal of the Rhombus is 12 cm . ❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$