Question : The diagonals of a rhombus are 12 cm and 16 cm, respectively. The length of one side is:
Option 1: 8 cm
Option 2: 6 cm
Option 3: 10 cm
Option 4: 12 cm
Correct Answer: 10 cm
Solution :
BD = 12 cm
AC = 16 cm
We know that the diagonals of rhombus bisect at $90^{\circ}$.
So, OD = $\frac{1}{2}$BD = 6 cm
AO = $\frac{1}{2}$AC = 8 cm
In $\triangle$AOD,
$\therefore$ Side, AD = $\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\ \text{cm}$
Hence, the correct answer is 10 cm.
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