Question

The area of a rhombus is 60cm square and one of it's diagonal is 4 cm .find the other diagonal?
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Answer 1

AnswEr :

• The other diagonal of a rhombus = 30 cm.

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Explanation :

We are given with the area of rhombus as well as one of it's diagonal, that is,

• Area of rhombus = 60 cm.

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• One diagonal of rhombus = 4 cm.

We have to find out the other diagonal of a rhombus$.$

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Now,

Let us assume that, x cm is the other diagonal of rhombus.

As we are given with the area of rhombus and one diagonal of a rhombus we kn the required formula, that is,

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→ Area of rhombus = ½ × d₁ × d₂.

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Substituting the given values in the formula,

⇒ 60 = ½ × 4 × x

⇒ 60 = 1 × 2 × x

⇒ 60 = 2 × x

⇒ 60 = 2x

⇒ 60/2 = x

⇒ 30 = x

Hence, the other diagonal of a rhombus is 30 cm.

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⠀⠀⠀ Additional information :

Some important properties of rhombus :

• A rhombus is also a quadrilateral.

• All straight sides of a rhombus are equal.

• The opposite sides of a rhombus are parallel.

• The opposite angles of a rhombus are equal.

• The sum of two adjacent angle is equal to the 180 degree.

• A rhombus diagonals bisect each other at right angle.

Answer 2

Given :-

❶ Area of rhombus = 60 cm

❷ Diagonal = 4 cm

To find :-

Other Diagonal

SoluTion :-

${\boxed {\boxed {\red { \tt Area = \frac{1}{2} \times d1 \times d2}}}} \:$

Let the second diagonal be x

☞ 60 = ½ × 4 × x

➵ 60 = 1 × 2 × x

➵ 60 = 2x

➵ x = 60÷2

➵ x = 30

➥ Other Diagonal = 30

Let's verify

☞ 60 = ½ × 30 × 4

➵ 60 = 15 × 4

➵ 60 = 60