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.​

Answer 1

Answer:

54 sq.cm

Step-by-step explanation:

Let the diagonals be 3x and 4x.

Given that:

4x=12cm (because 4x is larger than 3x and given that 12cm is the longer diagonal.)

To find:

Area of Rhombus.

Proof:

4x = 12

x =12/4

x = 3

3x = 3×3

3x = 9cm.

$area \: of \:rhombus \: = \frac{ab}{2}$

where, a and b are the two diagonals of the rhombus.

On substituting the values in the formula, we have,

$area \: of \: rhombus = \frac{12 \times 9}{2}$

$area \: of \: rhombus = 6 \times 9$

$area \: of \: rhombus = 54 {cm}^{2}$

Therefore, the area of the rhombus is 54 sq.cm

Hope it helps you.

Good Luck.

Answer 2

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 = (1/2) * Diagonal 1 * Diagonal 2.

➼ Area = (1/2) * 12 * 9

➼ Area = 6 * 9

Area = 54 cm².