Question

The length of the ears of any rhombus is 12 cm respectively. And 16 cm. If so, determine the arm length of the rhombus?​

Answer 1

Answer:

Given:-

Diagonals of a Rhombus =12cm and 16cm

To find:-

Side of the Rhombus

Solution:-

$\sf d_1=12cm$

$\sf d_2=16cm$

As we know that in a Rhombus

$\boxed{\sf Side_{(Rhombus)}=\dfrac {1}{2}\sqrt{d_1 ^2+d_2 ^2}}$

• Substitute the values

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow Side_{(Rhombus)}=\dfrac{1}{2}\sqrt {(12)^2+(16)^2}$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow Side_{(Rhombus)}=\dfrac {1}{2}\sqrt {144+256}$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow Side_{(Rhombus)}=\dfrac {1}{2}\sqrt {300}$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow Side_{(Rhombus)}=\dfrac {1}{2}\times 17.32$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow Side_{(Rhombus)}=8.66 cm$

Answer 2

Answer:

Answer:

Given:-

Diagonals of a Rhombus =12cm and 16cm

To find:-

Side of the Rhombus

Solution:-

\sf d_1=12cmd

1

=12cm

\sf d_2=16cmd

2

=16cm

As we know that in a Rhombus

\boxed{\sf Side_{(Rhombus)}=\dfrac {1}{2}\sqrt{d_1 ^2+d_2 ^2}}

Side

(Rhombus)

=

2

1

d

1

2

+d

2

2

Substitute the values

\begin{gathered}\\\qquad\quad\displaystyle\sf {:}\longrightarrow Side_{(Rhombus)}=\dfrac{1}{2}\sqrt {(12)^2+(16)^2}\end{gathered}

:⟶Side

(Rhombus)

=

2

1

(12)

2

+(16)

2

\begin{gathered}\\\qquad\quad\displaystyle\sf {:}\longrightarrow Side_{(Rhombus)}=\dfrac {1}{2}\sqrt {144+256}\end{gathered}

:⟶Side

(Rhombus)

=

2

1

144+256

\begin{gathered}\\\qquad\quad\displaystyle\sf {:}\longrightarrow Side_{(Rhombus)}=\dfrac {1}{2}\sqrt {300}\end{gathered}

:⟶Side

(Rhombus)

=

2

1

300

\begin{gathered}\\\qquad\quad\displaystyle\sf {:}\longrightarrow Side_{(Rhombus)}=\dfrac {1}{2}\times 17.32 \end{gathered}

:⟶Side

(Rhombus)

=

2

1

×17.32

\begin{gathered}\\\qquad\quad\displaystyle\sf {:}\longrightarrow Side_{(Rhombus)}=8.66 cm\end{gathered}

:⟶Side

(Rhombus)

=8.66cm

Step-by-step explanation:

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