Question

The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude are 24.8 cm and 16.5 cm respectively. If one of the diagonals of the rhombus is 22 cm, find the length of the other diagonal. fast fast !!!!!!!

Answer 1

Answer:

18.6 cm

Step-by-step explanation:

Given:

• The area of a rhombus is equal to the area of a triangle.
• Base of a triangle = 24.8 cm
• Height of a triangle = 16.5 cm
• One of the diagonals of the rhombus = 22 cm

To find:

• The length of the other diagonal.

Solution:

First find out the area of a triangle by using formula,

• Area of a triangle = 1/2 × b × h

Where,

• b is the base of a triangle.
• h is the height of a triangle.

Putting the values in the formula, we have:

• Area of a triangle = 1/2 × 24.8 × 16.5
• Area of a triangle = 409.2/2
• Area of a triangle = 204.6 cm²

Area of a rhombus = Area of a triangle

Now, we will find the length of other diagonal by using formula of area of rhombus.

Let the length of the other diagonal be x.

• Area of a rhombus = 1/2 × Product of its diagonals
• 204.6 = 1/2 × 22 × x
• 204.6 = 22/2 × x
• 204.6 = 11 × x
• x = 204.6/11
• x = 18.6 cm

∴ The length of the other diagonal = 18.6 cm

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