. The length of the diagonals of a
rhombus is 42 cm and 40 cm.
c
Find the perimeter of the
rhombus. (Hint: The diagonals
bisect each other at 90°)
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Let ABCD is the rhombus.
As we know that the diagonals of rhombus bisect each other at right angles,
So, AO = OC = 1/2AC = 1/2 × 42 cm = 21 cm.
and BO = OD = 1/2BD = 1/2 × 40 cm = 20 cm.
Angle DOC = 90°.
According to Pythagoras Theorem,
DC = √(21²+20²)
= √(441+400)
= √841
= 29
So, DC = side = 29 cm.
As all the sides of a rhombus are equal,
Perimeter = (29×4) cm = 116 cm.
Hence, the perimeter of the rhombus is 116 cm.
Hope this helps you to get to your answer.
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