In the given figure, ABCD is a rhombus, AO = 4 cm and DO = 3 cm. Then, find the perimeter of the rhombus.

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10cm

20cm

30cm

40cm

answer is B.

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Detailed Solution

AO = 4 cm and DO = 3 cm (Given)
We also know that the diagonals of a rhombus intersect at right angles.
As a result, the angles corresponding to O, such as AOD, AOB, and so on, are all right angles.
Now, we have got that ∠AOD=90

°

In △AOD:-
AD2 =AO2+DO2 (By Pythagorean Theorem)
⇒AD2 = 42+32
⇒AD2 = 16+9
⇒AD2 = 25
⇒AD = ±5
⇒AD = 5
Now, since we know that the sides of a rhombus are all equal.
Therefore, AB = BC = CD = AD.
Therefore, all the sides are 5 cm each.
Perimeter of a rhombus is 4 times side length which can be written as:-
⇒ Perimeter = 4×Side
⇒ Perimeter = 4×5
⇒ Perimeter = 20 cm
Hence, the answer is 20 cm.

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