Question

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The area of a rhombus is 240 cm2 and one of its diagonals is 16cm. Find its perimeter.​

Answer 1

Answer:

Area of rhombus=d1×d2/2

::240=16×d2/2

240×2/16=d2

30=d2

Diagonals AC=30cm and DB=16cm.

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

Therefore, OD= 2DB

16/2 =8cm

and OC= 2AC

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=root of 289 =17cm

Perimeter of the rhombus=4× side

=4×17=68cm

Thus, the perimeter of rhombus is 68 cm.

Hope, You will get it!!