Question

The diagonals of a rhombus are in the ratio 3:4.If the longer diagonal is 12cm,then find the area of rhombus


Plzz solve this guys​

Answer 1

• 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,

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

Hence, the value of x is 3 cm.

So,

The smaller diagonal of a rhombus = 3x

$\implies 3(3 \: cm) \\ \\ \implies3 \times 3 \: cm \\ \\ \implies9 \: cm$

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

Now we have,

• $\sf d_{1} = 9 \: cm$
• $\sf d_{2} = 12 \: cm$

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

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

Hence,

The area of a rhombus is 54 cm².

Answer 2

Given :-

• The diagonals of a rhombus are in the ratio 3:4.
• The longer diagonal is 12cm.

To Find :-

• Area of rhombus ?

Solution :-

Let us assume that, diagonals of a rhombus are 4x and 3x respectively.

As,

→ 4x > 3x.

So ,

→ Longer diagonal = 12cm.

→ 4x = 12cm.

dividing both sides by 4,

→ x = 3 .

Therefore,

→ Longer diagonal = 12cm.

→ shorter diagonal = 3x = 3 * 3 = 9cm.

Hence,

→ Area of rhombus = (1/2) * Diagonal 1 * Diagonal 2.

→ Area = (1/2) * 12 * 9

→ Area = 6 * 9

→ Area = 54 cm². (Ans.)

Some Properties of Rhombus :-

• All sides of the rhombus are equal.
• The opposite sides of a rhombus are parallel.
• Opposite angles of a rhombus are equal.
• In a rhombus, diagonals bisecting each other at right angles.
• Diagonals bisect the angles of a rhombus.
• The sum of two adjacent angles is equal to 180 degrees.
• The two diagonals of a rhombus form four right angled triangles which are congruent to each other.
• You will get a rectangle when you join the mid point of the sides.
• You will get another rhombus when you join the mid points of half the diagonal.
• Around a rhombus, there can be no circumscribing circle.
• Within a rhombus, there can be no inscribing circle.