Question

the area of rhombus is 28 metre square one of its diagonal 4 cm find the length of other diagona​

Answer 1

Given :

• Area = 28 m²
• Diagonal 1 = 4 cm

To Find :

• Diagonal 2 = ?

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$\dag$ 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

$\dag$ Calculating the Diagonal 2 :

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

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 28 \times 2 = 1 \times 4 \times D_2 } \; \qquad \bigg\lgroup {\purple{\sf{ 1 \; m = 100 \; cm }}} \bigg\rgroup \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 56 \times 100 = 4 \times D_2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { \dfrac{5600}{4} = D_2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { \cancel\dfrac{5600}{4} = D_2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\sf { Diagonal \; 2 = 1400 \; cm }}}}} \; {\red{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Second Diagonal of the Rhombus is 1400 cm .

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Answer 2

Given:-

• Area of rhombus = 28m²
• Diagonal 1= 4cm

To find:-

• Length of the other diagonal

Formula used:-

$\large \blue{\underline{ \green{ \boxed{\sf{ \red{ \implies{ \frac{1}{2} \times d_{1} \times d_{2} = area}}}}}}}$

Where,

$\large\underline{{ \boxed { \implies\sf{{ d_{1} = diagonal \: 1}}}}}$

$\large\underline{ \boxed{\sf{ \implies d_{2} = diagonal \: 2}}}$

Solution:-

We will put the values given in the question and will divide the area of rhombus from diagonal 1 to find the diagonal 2.We will first convert the m² to cm².Hence, To do this we have to multiply it with 10000.

Calculating for unit change:-

$\large\underline{\sf{ \implies1 {m}^{2} = 10000 {cm}^{2} }}$

$\large\underline{\sf{ \implies28 {m}^{2} = 28 \times 10000 {cm}^{2} }}$

$\large\underline{\sf{ \implies280000 {cm}^{2} }}$

Calculating for area :-

$\large\underline{\sf{ \implies\frac{1}{2} \times 4cm \times d_{2} = 280000 {cm}^{2} }}$

$\large\underline{\sf{ \implies2cm \times d_{2} = {280000cm}^{2} }}$

$\large\underline{\sf{ \implies d_{2} = \frac{280000 {cm}^{2} }{2cm} }}$

$\large\underline{\sf{ \implies d _{2} = 140000 {cm} }}$

We can convert this value in m²

$\large\underline{\sf{ \implies\frac{140000cm}{10000} }}$

$\large\underline{\sf{ \implies 14 {m}^{2} }}$

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Basic concept of rhombus:-

• A rhombus is a 2-D figure.
• It is a quadrilateral.
• It's opposite sides are parallel.
• It can be a Parallelogram.

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Deriviation of m² to cm²

• We know that 1m=100cm
• We also know that when we square a number it is multiplied by itself.
• So, 1m×1m=100cm×100cm
• Henceforth we get:- 1m²=10000cm².

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