Question

The diagonals of a rhombus are in ratio 3:4 if the longer diagonal is 12cm then find the are of rhombus​

Answer 1

Explanation:

The area of a rhombus = 54 cm².

Given :

The ratio of the diagonal of a rhombus = 3 : 4.

The length of the longer diagonal = 12 cm.

To Find :

The area of a rhombus.

Solution :

Let,

The smaller diagonal of a rhombus be 3x.

The longer diagonal of a rhombus be 4x.

We know that,

$\gray{ \boxed{ \orange{ \tt{Area \: of \: a \: rhombus = \dfrac{1}{2} \times d_{1} \times d_{2} }}}}$

First, we need to find the smaller diagonal of a rhombus.

Given,

The longer diagonal of a rhombus = 12 cm

That means,

$\begin{gathered} \implies4x = 12 \: cm \\ \\ \implies x = \cancel\dfrac{12}{4} \: cm \\ \\ \implies x = 3 \: cm \end{gathered}$

Hence, the value of x is 3 cm.

So,

The smaller diagonal of a rhombus = 3x

⟹3(3cm)

⟹3×3cm

⟹9cm

Hence, the diagonals of a rhombus are 12 cm and 9 cm

Now we have,

$\sf d_{1} = 9 \: cmd$

$\sf d_{2} = 12 \: cmd$

Now, substitute both the values of the diagonals in the formula of the area of a rhombus.

$\begin{gathered} \implies \dfrac{1}{ \cancel2} \times 9 \: cm \times \cancel{12} \: cm \\ \\ \implies1 \times 9 \times 6 \: {cm}^{2} \\ \\ \implies54 \: {cm}^{2} \end{gathered}$

Hence,

The area of a rhombus is 54 cm².

Answer 2

Answer:

Explanation:

The area of a rhombus = 54 cm².

Given :

The ratio of the diagonal of a rhombus = 3 : 4.

The length of the longer diagonal = 12 cm.

To Find :

The area of a rhombus.

Solution :

Let,

The smaller diagonal of a rhombus be 3x.

The longer diagonal of a rhombus be 4x.

We know that,

$\gray{ \boxed{ \orange{ \tt{Area \: of \: a \: rhombus = \dfrac{1}{2} \times d_{1} \times d_{2} }}}} </p><p>$

First, we need to find the smaller diagonal of a rhombus.

Given,

The longer diagonal of a rhombus = 12 cm

That means,

$\begin{gathered}\begin{gathered} \implies4x = 12 \: cm \\ \\ \implies x = \cancel\dfrac{12}{4} \: cm \\ \\ \implies x = 3 \: cm \end{gathered} \end{gathered} </p><p>$

Hence, the value of x is 3 cm.

So,

The smaller diagonal of a rhombus = 3x

⟹3(3cm)

⟹3×3cm

⟹9cm

Hence, the diagonals of a rhombus are 12 cm and 9 cm

Now we have,

$\sf d_{1} = 9 \: cm \\ </p><p></p><p>\sf d_{2} = 12 \: cm$

Now, substitute both the values of the diagonals in the formula of the area of a rhombus.

$\begin{gathered}\begin{gathered} \implies \dfrac{1}{ \cancel2} \times 9 \: cm \times \cancel{12} \: cm \\ \\ \implies1 \times 9 \times 6 \: {cm}^{2} \\ \\ \implies54 \: {cm}^{2} \end{gathered} \end{gathered} </p><p>$

Hence,

The area of a rhombus is 54 cm².