Question

The diagonals of a rhombus measure 16cm and 30cm. Find its perimeter

Answer 1

Step-by-step explanation:

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

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

Therefore, OD=

2

DB

=

2

16

=8cm

and OC=

2

AC

=

2

30

=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.

solution

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