Question

The area of rhombus is 120cm² and one of the diagonal is 8cm.Find the other diagonal.
ASN I Do no​

Answer 1

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Area of Rhombus = 120cm²

first daigonal = 8cm

${ \tt \red{area \: of \: rhombus = \frac{1}{2} \times \binom{d}{ \: \: 1} \times \binom{d}{ \: \: 2} \: }}$

$\tt {\: \: = > \: \: 120 = \frac{1}{ \cancel{2} } \times \cancel {8} \times \binom{d}{ \: \: 2} }$

$\tt{ \: \: = > \: \: \: \: \: \: \: \binom{d}{ \: \: \: 2} = \frac{ \cancel{120}}{ \cancel{4} }}$

$\: \: = > \: \: \: \: \: \: \: \tt {\binom{d}{ \: \: \: 2} = 30 \: cm}$

Hence, the diagonal is 30 cm.

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Answer 2

Answer:

Length of other diagonal = 30 cm

Step-by-step explanation:

Given :

Area of the Rhombus = 120 cm²

One diagonal = 8 cm

To find :

The length of other diagonal

Taken :

To find the length of other diagonal use the formula of the area of the rhombus -:

$\boxed{\sf{A=\dfrac{1}{2}\:\times\:d_{1}\:\times\:d_{2}}}$

Where,

A = Area of the Rhombus

$\sf{d_{1}}$ = One diagonal

$\sf{d_{2}}$ = Other diagonal

Solution :

$\leadsto\sf{{120cm}^{2}=\dfrac{1}{\cancel{2}}\times\cancel{8}cm\times\:d_{2}}$

$\leadsto\sf{{120cm}^{2}=4cm\times\:d_{2}}$

$\leadsto\sf{\dfrac{\cancel{{120cm}^{2}}}{\cancel{4cm}}=d_{2}}$

$\leadsto\sf{30cm=d_{2}}$

So , the length of other diagonal is 30 cm .