# 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.?

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$\\\bigtriangleup AOB,\\ \\\Rightarrow \angle AOB=90^{\circ}$

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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