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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Question : The area of the rhombus is 216 cm2 and the length of its one diagonal is 24 cm. The perimeter (in cm) of the Rhombus is:
Option 1: 52
Option 2: 60
Option 3: 120
Option 4: 100
Question : The length of the diagonals of a rhombus is 40 cm and 60 cm. What is the length of the side of the rhombus?
Option 1: $50 \sqrt{3} \ \text{cm}$
Option 2: $20 \sqrt{3}\ \text{cm}$
Option 3: $10 \sqrt{13}\ \text{cm}$
Option 4: $40 \sqrt{13}\ \text{cm}$
Question : What is the area of a rhombus whose diagonals are 8 cm and 13 cm?
Option 1: 52 cm2
Option 2: 96 cm2
Option 3: 44 cm2
Option 4: 84 cm2
Question : The perimeter of a rhombus is 100 cm and one of its diagonals is 40 cm. Find its area.
Option 1: 1200 cm2
Option 2: 1000 cm2
Option 3: 600 cm2
Option 4: 500 cm2
Question : The area and the length of one of the diagonals of a rhombus are 84 cm2 and 7 cm respectively. Find the length of its other diagonal (in cm).
Option 1: 12
Option 2: 24
Option 3: 48
Option 4: 36
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