Question

ABCD is a rhombus of side 20 cm and has two angles of ${60}^{\circ }$ each. The length of the diagonal AC is:

• A. 10 cm
• B. 20 cm
• C. 15 cm
• D. None of these

Answer 1

The correct option is B 20 cm

Given: A rhombus with side 20 cm and a pair of opposite angle as ${60}^{\circ }$

Consider a rhombus ABCD

$Sin30=\frac{AE}{AB}=\frac{AE}{20}\frac{1}{2}=\frac{AE}{20}\Rightarrow AE=10\Rightarrow AC=2AE$ [$\because$ Diagonals of a rhombus bisect each other]
$\therefore AC=20cm$