Question

The area of a rhombus is 36 cm. If one diagonal is 12 cm, find the length of the
other diagonal​

Answer 1

Correct Question

• The area of a rhombus is 36 cm². If one diagonal is 12 cm, find the length of the other diagonal?

Given:

• One Diagonal = 12 cm
• Area = 36 cm²

To Find:

• Length of the other diagonal?

Formula Used:

$\\ \bigstar{\underline{\boxed{\tt\large{ \green{Area_{(Rhombus)} } = \dfrac{1}{2} d_{1} d_{2} }}}}$

Where

• d¹ = One diagonal
• d² = Other diagonal

Solution:

After substituting values,

$\implies$ a = ½ (d¹ × d²)

$\implies$ 36 = ½ (12 × d²)

$\implies$ 36 = 6 × d²

$\implies$ 36/6 = d²

$\implies$ d² = 6 cm

Hence,

• The Length of the Other diagonal of the Rhombus is 6 cm.

$\bigstar{\underline{\tt\pink{ Formula \ related \ to \ Rhombus :- }}}$

$\\ \bullet \: \: {\sf\red{ Area_{(Rhombus)} = \dfrac{1}{2} d_{1} d_{2} }} \\ \\ \bullet \: \: {\sf\red{ Perimeter_{(Rhombus)} = 4a }} \\ \\ \bullet \: \: {\sf\purple{ Diagonal = \sqrt{ 4a^2 - d^2 } }}$

Answer 2

Given:

• The area of a rhombus is 36 cm
• One diagonal is 12 cm

To Find:

• The length of the other diagonal

Solution:

$Area \: \: of \: \: Rhombus = \frac{1}{2} \times product \: of \: diagonals$

$Area \: \: of \: \: Rhombus = \frac{1}{2} \times d \times 12 \\36 = d \times 12 \\ </strong><strong>2</strong><strong>d = 3 \: cm$

Length of diagonal is 6 cm.

Extra Information:

• The area of a rhombus can be defined as the amount of space enclosed by a rhombus in a two-dimensional space.

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