Question

Find the perimeter of a rhombus, the lengths of whose diagonals are
16 cm and 30m. ​

Answer 1

Answer:

Step-by-step explanation:

Given Diagonals of rhombus,

= 16 cm and 30 cm

To Find,

Perimeter of rhombus

Formula to be used,

Pythagoras theorem.

Perimeter of the rhombus i.e 4 × side

Solution,

Here,

The diagonals of the rhombus bisect at a right angle to each other.

Then,

OD = DB/2 = 16/2 = 8 cm

OC = AC/2 = 30/2 = 15 cm

Now,

By applying Pythagoras theorem, we get

In right angled ΔDOC

⇒ DC² = OD² + OC²

⇒ DC² = (8)² + (15)²

⇒ DC² = 64 + 225

⇒ DC² = 289

⇒ DC = √289 cm

Now,

⇒ Perimeter of the rhombus = 4 × side

⇒ Perimeter of the rhombus = 4 × 17

⇒ Perimeter of the rhombus = 68 cm

Hence, the perimeter of the rhombus is 68 cm.

Answer 2

$\huge\sf{Answer :- }$

Given :-

Diagonals of Rhombus

• AC = 30cm

• DB = 16cm

To Find :-

• Side of the rhombus

• Perimeter of the rhombus

Solution :-

we know that,

The diagonals of rhombus are bisect at the right angle to each other,

➣ So, OD = DB/2

16/2 = 8cm

∴ OD = 8cm

➣ OC = AC/2

30/2 = 15cm

∴ OC = 15cm

Now , By using Pythagoras theorem,

we get right- angled triangle ∆DOC

(DC)² = (OD)² + (CO)²

By substituting values,

➙ (DC)² = (8cm)² + (15cm)²

➙ (DC)² = 64 + 225

➙(DC)² = 289

➙ DC = √289

➥ DC = 17cm

Hence, The side of the rhombus is 17cm

Perimeter of the rhombus = 4 × side

➙ 4 × 17cm

➠ 68cm

Hence , The Perimeter of the rhombus is 68cm