Ans.Q.8. Perimeter of a rhombus is 146 cm andthe length of one of its diagonals is 48 cm. Findthe length of its other diagonal.?

Answers (1)

Solution: 

All sides of a rhombus are equal.

Length of each\ =146/4=36.5 

Diagonals in a rhombus bisect each other at right angles.

O is the midpoint of AC and  BD 

And 

BD=55

Therefore, OB=OD=27.5

By pythagoras theorem,

In\igtriangleup AOB,\ \Rightarrow angle AOB=90^circ

 

So,

\AB^2=AO^2+OB^2\ \Rightarrow (36.5)^2=AO^2+(27.5)^2\ \Rightarrow AO=24

Length of diagonal AC=24+24=48

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