Question

The measure of each of the two opposite angles of a rhombus is ${60}^{\circ }$ and the measure of one of its sides is $10cm$. The length of its smaller diagonal is:

• A. $10cm$
• B. $10\sqrt{3}cm$
• C. $10\sqrt{2}cm$
• D. $\frac{5}{2}\sqrt{2}cm$

Answer 1

Answer: (A)

$10cm$

Let $\angle B=\angle D={60}^{\circ }$
In $\Delta ADC,$
$AD=DC$ ...(adjacent sides of a rhombus)
$\Rightarrow \angle ACD=\angle DAC=\frac{180-{60}^{\circ }}{2}={60}^{\circ }$ ...(Isosceles $\Delta$ Property)
$\therefore \Delta ADC$ is an equilaterial triangle
$\Rightarrow AC=AD=DC-10cm.$