Question : If the diagonals of a Rhombus are 12 cm and 16 cm, then what is the perimeter (in cm) of the Rhombus?
Option 1: 20 cm
Option 2: 40 cm
Option 3: 60 cm
Option 4: 80 cm
Correct Answer: 40 cm
Solution :
The diagonals of a rhombus are 12 cm and 16 cm.
We know that diagonals perpendicularly bisect each other in a rhombus.
Side of a rhombus = $\sqrt{(\frac{\text{Diagonal_1}}{2})^2 + (\frac { \text{Diagonal_2}}{2})^2}$
⇒ Side of rhombus = $\sqrt{(\frac{12}{2})^{2}+ (\frac{16}{2})^{2}}$
⇒ Side = $\sqrt{36+64} = \sqrt{100} = 10$ cm
$\therefore$ Perimeter = 4 × 10 = 40 cm (Since all sides are equal in a rhombus)
Hence, the correct answer is 40 cm.
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