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The diagonals of a rhombus measure 16 cm and 30 cm .find its perimeter ( in easy way)?

User Borzio
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1 Answer

11 votes
11 votes

Answer:

68 cm

Explanation:

Let ABCD be a rhombus, all sides of the rhombus have equal length and its diagonal AC and BD are intersecting each other at a point O.

As we know that the diagonals in the rhombus bisect each other at 90°.

So, AO can be written as (AC/2)

= 16/2

= 8 cm

And, DO can be written as (BD/2)

= 30/2

= 15 cm

Then, consider the triangle AOD and apply Pythagoras theorem,

AD2 = AO2 + DO2

AD2 = 82 + 152

AD2 = 64 + 225

AD2 = 289

AD = √289

AD = 17 cm

Hence, the length of each side of the rhombus is 17 cm

Now,

The perimeter of rhombus = 4 × side of the rhombus

= 4 × 17

= 68 cm

Therefore, the perimeter of the rhombus is 68 cm.

User JuanR
by
3.1k points