Question : If the diagonals of a rhombus are 16 cm and 30 cm. What is the perimeter (in cm) of the rhombus?
Option 1: 32 cm
Option 2: 64 cm
Option 3: 34 cm
Option 4: 68 cm
Correct Answer: 68 cm
Solution :
The diagonals of a rhombus are 16 cm and 30 cm.
We know 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 = $\sqrt{(\frac{16}{2})^{2}+ (\frac{30}{2})^{2}}$
⇒ Side = $\sqrt{82+152} = \sqrt{289} = 17$ cm
$\therefore$ Perimeter = 4 × 17 = 68 cm (Since all sides are equal in a rhombus)
Hence, the correct answer is 68 cm.
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