Question

A parallelogram given and it's diagonal 16cm and 30cm. Find its perimeter

Answer 1

Given: Diagonals AC=30cm and DB=16cm.

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

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

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

Now, In right angle triangle DOC,

(DC)²=(OD)²+(CO)²

⇒(DC)² =(8)²+(15)²

⇒(DC)² =64+225=289

⇒DC= √289=17cm

Perimeter of the rhombus=4× side

=4×17=68cm

Thus, the perimeter of rhombus is 68 cm.

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