Question

The diagonal of a rhombus are in ratio 2:3 ,If the area is 121.5 cm square ,find the length of the diagonal​

Answer 1

Given,

• The diagonal of a rhombus are in ratio 2:3.
• Area of rhombus 121.5 cm².

To Find,

• The length of the diagonal.

According to question,

Let the diagonal of rhombus are 2x and 3x.

We know that,

Area of rhombus = ¹/2 × d1 × d2

Here,

• d1 = First Diagonal
• d2 = Second diagonal

[ Put the values ]

⟶ 121.5 = ¹/2 × 2x × 3x

⟶ 121.5 × 2 = 6x²

⟶ 243 = 6x²

⟶ x² = 243/6

⟶ x² = 40.5

⟶ x = 6.36 cm

Therefore,

Diagonals of rhombus,

• First diagonal = 2x = 2 × 6.36 = 12.72 cm.
• Second diagonal = 3x = 3 × 6.36 = 19.08 cm.

Answer 2

Given, the diagonal of a rhombus are in ratio 2:3 , and the area is 121.5 cm square.

☯we need to find the length of the diagonal.

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Let the ratio of diagonals (d1 and d2) of a rhombus be 2x and 3x.

We know that,

⠀

$\star\;{\boxed{\sf{\purple{Area_{(rhombus)} = \frac{1}{2} \times {d}^{1} \times {d}^{2} }}}}$

Putting values,

$:\implies\sf 121.5 = \frac{1}{2} \times 2x \times 3x$

$:\implies\sf 121.5 2 \times = {6x}^{2}$

$:\implies\sf 243 = 6x^2$

$:\implies\sf {x}^{2} = {\cancel \frac{243}{6}}$

$:\implies\sf x^2 = 40.5$

$:\implies{\boxed{\frak{\pink{x = 6.36 cm }}}}\;\bigstar$

Therefore, measure's of the diagonals of rhombus are,

First diagonal = 2x = 2 × 6.36 = 12.72 cm.

Second diagonal = 3x = 3 × 6.36 = 19.08 cm

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━