If the diagonals of a rhombus are 41 cm and 40 cm. What is the perimeter?

Given: If the diagonals of a rhombus are 41 cm and 40 cm.

To find: Here we have to find the perimeter of the given rhombus.

Solution:

The diagonals of a rhombus divide themselves into two equal segments and they would divide the rhombus itself into four congruent right triangles, with the side of the rhombus becoming the hypotenuse.

Using Pythagoras theorem in ∆AOD:

AD² = AO² $+$ DO²  

AD² = (20)² $+$ (20.5)²  

AD² = 400 $+$ 420.25  

AD² = 820.25  

AD = $\sqrt{820.25}$  

AD = 28.64 cm 

Now, 

Perimeter of a rhombus = 4 $\times$ (Length of the side)

Perimeter of a rhombus = 4 $\times$ (28.64) cm

Perimeter of a rhombus = 114.56 cm

So, perimeter of the rhombus is 114.56 cm

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Updated on: 10-Oct-2022

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