Question

The area of a rhombus is 480cm² and one of its diagonals measures 48cm. find (i) the length of the other diagonal, (ii) the length of each of its sides, and (iii) it's perimeter​

Answer 1

Answer :

1. Length of the other diagonal = 20cm
2. Length of each of its sides = 26cm
3. It's perimeter = 104cm

Given :

• The area of a rhombus is 480cm² and one of its diagonals measures 48cm.

To Find :

1. The length of the other diagonal.
2. Length of each of it's sides.
3. It's perimeter.

Solution :

Here

• Area of a rhombus is 480cm².
• One of the diagonal measures 48cm.

As we know that

• Area of a rhombus is ½ × d1 × d2

Now

→ ½ × d1 × d2 = 480

→ ½ × 48 × d2 = 480

→ 24 × d2 = 480

→ d2 = 480/24

→ d2 = 20

Half of the two diagonals and side make a right triangle

• a² + b² = c²

Where

• a = d1/2
• b = d2/2
• c = side

Now

→ side² = (48/2)² + (20/2)²

→ side² = (24)² + (10)²

→ side² = 576 + 100

→ side² = 676

→ side = √676

→ side = 26cm

As we know that

• Perimeter of a rhombus is 4 × side

Now

→ Perimeter of the rhombus = 4 × side

→ Perimeter of the rhombus = 4 × 26

→ Perimeter of the rhombus = 104cm

Hence,

1. Length of the other diagonal = 20cm
2. Length of each of its sides = 26cm
3. It's perimeter = 104cm