Question

the diagonals of a rhombus are in the ratio 3:4. if the longer diagonal is 12 cm then find the area of the rhombus. Pls add step by step explanation​

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,

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

Given,

The longer diagonal of a rhombus = 12 cm

That means,

Hence, the value of x is 3 cm.

So,

The smaller diagonal of a rhombus = 3x

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

Now we have,

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

Hence,  the area of a rhombus is 54 cm².