Question

area of rhombus is 120 cm sq. and one diagonal is 8 CM so, please find the other side of diagonal

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Answer 1

☞︎︎︎ Given :

$\:$

• Area = 120cm²

• length of diagonal = 8cm

☆ Solution :

$\:$

$\large \red{\rightarrow} \: \boxed{\mathrm{area = \dfrac{1}{2} \times d_1 \ \: \times d_2}}$

$\:$

$\large\implies \mathtt{120 = \dfrac{1}{2} \times 8 \times d_2}$

$\:$

$\large\implies \mathtt{120 = \dfrac{1}{ \cancel{2}} \times \cancel8 \times d_2}$

$\:$

$\large \implies \: \mathtt{120 =4 \times d_2}$

$\:$

• On Transposing The Terms :

$\large\implies \mathtt{d_2 = \dfrac{120}{4} }$

$\:$

$\large\implies \mathtt{d_2 = \dfrac{ \cancel{120}}{ \cancel4} }$

$\:$

$\large\implies \mathtt{d_2 = 30cm}$

$\:$

∴ Another diagonal = 30cm

Answer 2

Answer :-

• Second Diagonal of Rhombus = 30 cm

Given :-

• Area of Rhombus = 120 cm²
• First Diagonal of Rhombus = 8 cm

To Find :-

• Second Diagonal of Rhombus = ?

Explanation :-

Let the Second Diagonal of Rhombus to be 'x' cm

As we know,

$\pink \bigstar \: { \underline { \boxed { \bf \implies Area \: of \: Rhombus = \dfrac{1}{2} \times D_1 \times D_2 }}} \: \bigstar$

Now Substituting the values,

$\rm : \: \longrightarrow \dfrac{1}{2} \times D_1 \times D_2 = Area \: of \: Rhombus$

$\rm : \: \longrightarrow \dfrac{1}{2} \times 8 \times x = 120 \: cm^2$

$\rm : \: \longrightarrow x = \dfrac{120 \times 2}{8} \: cm^2$

$\rm : \: \longrightarrow x = \dfrac{240}{8} \: cm^2$

$\red { \underline { \boxed { \bf : \: \longrightarrow x = 30 \: cm }}}$

Hence, the Second Diagonal of the Rhombus is 30 cm.

@Agamsain