Question

The diagonals of a rhombus are of length 6 cm and 8 cm. Find the length of its side and also find its perimeter.

Answer 1

Answer:

5cm perimeter=20 cm

Step-by-step explanation:

Diagonals of a rhombus bisect each other at right angles and 4 triangles would be formed.

in one the triangles, the right angle will have sides 3 and 4 cm

so the hypotenuse i.e one side will be 5 cm

and perimete=4*5

=20 cm

Answer 2

${ \text{ \red{ \underline{ \purple{ \underline{Given data}}}}}:-}$

◐ The diagonals of a rhombus are of length 6 cm and 8 cm.

${ \text{ \red{ \underline{ \purple{ \underline{Solution}}}}}:-}$

◐ We know that diagonal of rhombus, bisect each other in right angle ( 90° ) in equal length.

◐ We also know that all sides of rhombus are equal ( of equal length ).

So, now

Let rhombus is ABCD {according to figure}

Let, diagonal of rhombus

BD = 8 cm and AC = 6 cm

means,

OD = 4 cm and AO = 3 cm

By pythagorus theorem

To find length of AD ( and all side of rhombus )

→ (AD)² = (OD)² + (AO)²

→ (AD)² = (4)² + (3)²

→ (AD)² = 16 + 9

→ (AD)² = 25

→ AD = √25

→ AD = 5 cm

Now,

→ Perimeter of rhombus = 4 × ( side )

→ Perimeter of rhombus = 4 × ( AD )

→ Perimeter of rhombus = 4 × 5

→ Perimeter of rhombus = 20 cm

Hence, length of all side of rhombus is 5cm and perimeter of rhombus is 20cm.