Question

The perimeter of the rhombus is164 cm and the length of one diagonal is 18cm find the length of other diagonal.​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

We know that in a rhombus all the sides are equal.

Therefore length of each side = Perimeter/ 4 =

164/4= 41cm

Length of one diagonal = 18 cm

Now , we know that diagonals of a rhombus bisect each other at right angles .

Please refer to the attachment for the figure of the rhombus for clear understanding.

In right triangle AOD-

AD(Hypotenuse)= 41cm

OD=18/2=9cm

Therefore,

AO^2=AD^2-OD^2 ( According to Pythagoras theorem)

AO^2=41^2- 9^2

AO^2=1681-81

AO^2= 1600

Therefore, AO =

$\sqrt{1600} = 40cm$

Now Length of diagonal AC = 2 AO = 2×40= 80 cm

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