Question

If the area of the rhombus is 96 cm sq and its diagonal is 12 cm long. Find the length of the other diagonal​

Answer 1

Answer:

P(Diagonal)= 12cm

A(Area)= 96cm

2

Using the formula

A=

2

Pq

q= 4a

a=

2

2

P 2

P=

2P

2

+4

(

P

A

)

2

= 2

12 2

(

1 2

9 6

)

2

=

40 cm.

Step-by-step explanation:

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Answer 2

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

⠀ • Area of a rhombus is 96$cm^2$ ⠀

• one of the diagonal is 12 cm.

$\sf{\bold{\red{\underline{\underline{To\:Find}}}}}$

▪length of the other diagonal of rhombus. ⠀⠀⠀⠀

$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

Here,

⠀⠀⠀⠀

Area of a rhombus is 96$cm^2$ ⠀

And ,one of the diagonal =$\tt{d_1=12cm. }$ ⠀

Let, other diagonal of that rhombus =$\tt{d_2=x }$ ⠀

we know that,

$\boxed{\underline{\underline{\mathcal\color{fuchsia}{A=\dfrac{1}{2}×d_1×d_2}}}}$

where,

$\textsf{A=area of rhombus. }$ ⠀

$\tt{ d_{1}~~ and ~~d_{2 }~~are ~two ~diagonals }$

so,

According to the question;

$\leadsto$ $\tt{\dfrac{1}{2}×12×x\implies{96} }$ ⠀

$\rightsquigarrow$ $\tt{\dfrac{1}{\cancel{2}}×\cancel{12}×x\implies{96} }$ ⠀

$\hookrightarrow$ $\tt{6x\implies{96} }$ ⠀

$\rightsquigarrow$ $\tt{x\implies{\dfrac{96}{6}} }$ ⠀

$\hookrightarrow$ $\tt{x\implies{\dfrac{\cancel{96}}{\cancel{6}}} }$ ⠀

$\longrightarrow$ $\tt{x\implies{16} }$ ⠀

$\therefore$ The other diagonal of that rhombus is $\tt{\pink{16~cm.} }$ ⠀

⠀