Question

Find the area of a rhombus whose one side is 5cm and whose altitude is 4.8cm. If one of its diagonals is 8cm long,find the length of the other diagonal.

Answer 1

Answer:

6 cm

Step-by-step explanation:

Area of the rhombus = Side × Length of the altitude 

= 5*4.8

= 24 sq cm 

Now,

Let the length of the other diagonal = x

It is known that the area of a rhombus is half the product of its diagonals. 

∴ (1/2) × 8 × x = 24

⇒ 4x = 24

⇒ x = 6 cm

The length of the other diagonal is 6 cm.

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Answer 2

Given:-

• The area of rhombus, side is 5cm and altitude is 4.8cm and one of its diagonal is 8cms.

To Find:-

• Find the length of other diagonal. ....?

Solutions:-

• Let the length of the other diagonal of the rhombus be x.

• A rhombus is a special are of a parallelogram.

• The area of a parallelogram is the product of its base and height.

Area of the Rhombus = base × height

= 5cm × 4.8cm

= 24cm²

Area of rhombus = 1/2 (products of its diagonal)

⟹ 24cm² = 1/2 × (8cm + x)

⟹ x = 24 × 2 / 8

⟹ x = 48/8

⟹ x = 6cm

Hence, the length of the other diagonal of the Rhombus is 6cm.

Some Important:-

• A rhombus all side are equal.
• A rhombus opposite angle are equal.
• A rhombus the sum of adjacent angle angle supplementary i.e. (<A + <D = 180°).
• A rhombus, each diagonal of a rhombus divides it into two congruent triangle.
• A rhombus, if one angle is right, then all angle are right.
• Diagonal of a rhombus bisect each other and also perpendicular to each other.

More important:-

1. Area of rhombus = b × h
2. Perimeter of rhombus = 4 × side

where,

• b = base
• h = height
• p = perimeter
• a = area