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
Option 2: 64
Option 3: 34
Option 4: 68
Correct Answer: 68
Solution :
The diagonals of a Rhombus are 16 cm and 30 cm.
We know diagonals perpendicularly bisect each other in a Rhombus.
Side of Rhombus = hypotenuse of the triangle formed by the halves of the diagonals.
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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