One of the diagonals of a rhombus of area 24 sq m is 6m what is the length of its other diagonal?

A rhombus is a diamond-shaped quadrilateral with equal sides but unequal angles of inclination between these two sides. It has four sides that are all the same length since it is a quadrilateral. It can be said that the rhombus is a specific type in a parallelogram, if all the sides of the parallelogram are to be equal, it will become a shape known as a rhombus.

By using Diagonals Area of Rhombus:  = (d₁ × d₂)/2 sq. units.

Where d₁ is the length of diagonal 1 and d₂ is the length of diagonal 2.

One of the diagonals of a rhombus of an area of 24 sq m is 6m what is the length of its other diagonal?

Solution:

To find the length of diagonal d_2,

Area of Rhombus = 24 sq m 

Length of diagonal d₁ = 6 m

Therefore, Area of Rhombus = (d₁ × d₂)/2 sq. units

24  =  (6 × d₂) / 2

24  =  3d₂

d₂ = 24/3

d₂ = 8 m

So the length of diagonal d₂ is 8 m.

Sample Questions 

Question 1:  Calculate the area of a rhombus (using diagonal) having diagonals equal to 5 cm and 4 cm.

Solution:

Given,

Length of diagonal 1 (d₁) = 5 cm

Length of diagonal 2 (d₂) = 4 cm

Now,

Area of Rhombus (A) = 1/2 d₁ × d₂

= 1/2  × 5 × 4

= 1/2 × 20 

= 10 cm²

Question 2: Find the diagonal of a rhombus if its area is 100 cm² and the length measure of the longest diagonal is 10 cm.

Solution:

Given: Area of rhombus = 100 cm² and Diagonal d₁ = 10 cm.

Hence, Area of the rhombus formula, A = (d₁ × d₂)/2 square units, we get

100 = (10 × d₂)/2

100 = 10 d₂ / 2

Or 5d₂ = 100

d₂ = 20

Therefore, the Length of another diagonal d₂ is 20 cm.

Question 3: Calculate the area of a rhombus whose diagonals are of the lengths 15 cm and 4 cm?

Solution:

Given: Diagonal d₁ = 15 cm

Diagonal d₂ = 4 cm

Area of a rhombus, A = (d₁ × d₂) / 2

= (15 × 4) / 2

= 60/2

= 30 cm²

Hence, the area of a rhombus is 30 cm².

Question 4:  Find the area of the rhombus where the side of the rhombus is 4 cm and one of the interior angles is 30°.

Solution:

Given,

Side length = 4 cm

Interior angle = 30°

Using Trigonometry , Area of rhombus = (side)² Sin(30°)

= 4² × sin(30°)

= 16 × (1/2)

= 8 cm²

So the area of Rhombus is 8 cm². 

Question 5: Find the perimeter of a rhombus whose side is 6 cm.

Solution: 

Given side s = 6 cm

Therefore, Perimeter of Rhombus = 4 × s

So, Perimeter (P) = 4 × 6 cm 

= 24 cm

Question 6: One of the diagonals of a rhombus of area 30 sq m is 6m what is the length of its other diagonal?

Solution: 

To find the length of diagonal d₂,

Area of Rhombus = 30 sq m

Length of diagonal d₁ = 6 m

Therefore, Area of Rhombus  = (d₁ × d₂)/2 sq. units

30 = (6 × d₂) / 2

30  =  3d₂

d₂ = 30/3

d₂ = 10 m

So the length of diagonal d₂ is 10 m.

Question 7: Find the height of the rhombus whose area is 200 m² and the perimeter is 100 m?

Solution:

Given, the perimeter of the rhombus = 120 m

So, side of rhombus = 100/4 

= 25 m

We know that the area of Rhombus = b × h

Therefore the height is, 200 = 25 × h

h = 200 /25

h = 8

Therefore, the height of the rhombus is 8 m.

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