Question

find the perimeter of a rhombus the length of whose diagonals are 16 cm and 30 cm

Answer 1

I have given the answer in the above picture.

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Answer 2

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, perimeter of rhombus is 68 cm ✝

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