Question

Construct a rhombus whose one diagonal is of length $8cm$ and the angle made by the sides at the end points of this diagonal is ${60}^{\circ }$. The length of the other diagonal is:

• A. $2.3cm$
• B. $4.6cm$
• C. $6.9cm$
• D. $13.8cm$

Answer 1

The correct option is B $4.6cm$

$\Rightarrow$ We know that all sides of rhombus are equal and opposite angles are equal.

$\Rightarrow$ Diagonals of rhombus bisect angles equally.

$\Rightarrow$ Draw a line segment AC = 8cm.

$\Rightarrow$ Construct an angle of ${30}^{\circ }$ above and below at point A.

$\Rightarrow$ Similarly, construct an angle of ${30}^{\circ }$ above and below at point C which is meeting at previous at angle at point B and D.

$\Rightarrow$ So, we get $\angle BAD={60}^{\circ }$ and $\angle BCD={60}^{\circ }$

$\Rightarrow$ Thus, ABCD is a required rhombus.

$\Rightarrow$ We have to measure length other diagonal which is BD.

$\therefore$ $l\left(BD\right)=4.6cm$