Question : If ABCD is a rhombus, AC is its smallest diagonal, and $\angle$ABC = $60^{\circ}$, find the length of a side of the rhombus when AC = 6 cm.
Option 1: $6$ cm
Option 2: $3$ cm
Option 3: $6\sqrt2$ cm
Option 4: $3\sqrt3$ cm
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Correct Answer: $6$ cm
Solution : In rhombus ABCD, AB = BC = CD = DA AC = 6 cm $\angle$ABC = $60^{\circ}$ In $\triangle$ABC, AB = BC So, $\angle$BAC = $\angle$BCA Now, $\angle$BAC + $\angle$BCA + $\angle$ABC = $180^{\circ}$ ⇒ $\angle$BAC + $\angle$BCA = $120^{\circ}$ ⇒ $\angle$BAC = $\angle$BCA = $\angle$ABC = $60^{\circ}$ ⇒ $\triangle$ABC is an equilateral triangle. ⇒ AB = BC = AC = 6 cm Hence, the correct answer is $6$ cm.
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Question : The length of each side of a rhombus is equal to the length of the side of a square whose diagonal is $40\sqrt2$ cm. If the length of the diagonals of the rhombus is in the ratio $3:4$, then its area ( in cm2) is:
Question : The side $BC$ of a triangle $ABC$ is extended to $D$. If $\angle ACD = 120^{\circ}$ and $\angle ABC = \frac{1}{2} \angle CAB$, then the value of $\angle ABC$ is:
Question : In a $\triangle ABC$, if $2\angle A=3\angle B=6\angle C$, then the value of $\angle B$ is:
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:
Question : If the perimeter of an equilateral triangle is 18 cm, then the length of each median is:
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