Question

Construct a rhombus $ABCD$ with $AC=7cm$ and $m\angle BAD={120}^{\circ }$. Then the length of the side of the rhombus is:

• A. $4cm$
• B. $7cm$
• C. $10cm$
• D. $14cm$

Answer 1

The correct option is B $7cm$

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

$\Rightarrow$ Diagonals of rhombus bisect angles equally.

$\Rightarrow$ Draw a line segment AC = 7cm.

$\Rightarrow$ Construct an angle of ${60}^{\circ }$ above and below at point A.

$\Rightarrow$ Similarly, construct an angle of ${60}^{\circ }$ above and below at point C, which is meeting at previous angle at point B and D.

$\Rightarrow$ So, we get $\angle BAD={120}^{\circ }$ and $\angle BCD={120}^{\circ }$

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

$\Rightarrow$ We have to measure length sides of rhombus which are AB, BC, CD and AD.

$\Rightarrow$ $l\left(AB\right)=l\left(BC\right)=l\left(CD\right)=l\left(AD\right)=7cm$