Question : The diagonals of a rhombus are 12 cm and 16 cm, respectively. The length of one side is:
Option 1: 8 cm
Option 2: 6 cm
Option 3: 10 cm
Option 4: 12 cm
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Correct Answer: 10 cm
Solution : BD = 12 cm AC = 16 cm We know that the diagonals of rhombus bisect at $90^{\circ}$. So, OD = $\frac{1}{2}$BD = 6 cm AO = $\frac{1}{2}$AC = 8 cm In $\triangle$AOD, $\therefore$ Side, AD = $\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\ \text{cm}$ Hence, the correct answer is 10 cm.
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Question : If the diagonals of a rhombus are 8 cm and 6 cm, then the square of its side is:
Option 1: $25\;\mathrm{cm^2}$
Option 2: $55\;\mathrm{cm^2}$
Option 3: $64\;\mathrm{cm^2}$
Option 4: $36\;\mathrm{cm^2}$
Question : The area of a rhombus is 256 square cm, and one of its diagonals is twice the other in length. The length of its larger diagonal is:
Option 1: 32 cm
Option 2: 16 cm
Option 3: 48 cm
Option 4: 24 cm
Question : Three cubes of iron whose edges are 6 cm, 8 cm, and 10 cm, respectively, are melted and formed into a single cube. The edge of the cube formed is:
Option 1: 12 cm
Option 2: 14 cm
Option 3: 16 cm
Option 4: 18 cm
Question : Two concentric circles are of radii 10 cm and 6 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Option 3: 12 cm
Option 4: 9 cm
Question : The lengths of the diagonals of a rhombus are 24 cm and 10 cm, then the perimeter of the rhombus (in cm) is:
Option 1: 52
Option 2: 56
Option 3: 68
Option 4: 72
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