Question : If the diagonals of a rhombus are 10 cm and 24 cm, then what is the perimeter of the rhombus?
Option 1: 50 cm
Option 2: 60 cm
Option 3: 56 cm
Option 4: 52 cm
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Correct Answer: 52 cm
Solution :
In a rhombus, the diagonals bisect each other at right angles.
Therefore, we can form a right-angle triangle using half of each diagonal as the sides.
Let the half diagonals as $a$ and $b$.
$⇒a = \frac{10}{2} = 5 \text{ cm}$
$⇒b = \frac{24}{2} = 12 \text{ cm}$
Using the Pythagorean theorem,
$\text{Side} = \sqrt{a^2 + b^2} = \sqrt{5^2 + 12^2} = \sqrt{169} = 13 \text{ cm}$
The perimeter of a rhombus is four times the length of a side,
Perimeter = 4 × Side = 4 × 13 = 52 cm
Hence, the correct answer is 52 cm.
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