Question

Can we construct a rhombus $ABCD$ with $AB=4cm$? Its diagonal intersect at the point $O$ and $\angle OAB={60}^0$.

• A. Yes
• B. No
• C. Sometimes yes
• D. Can't say

Answer 1

The correct option is A Yes

Given : $AB=4$cm

Diagonal intersect at $O$ and $\angle OAB={60}^o$ ....... $\left(1\right)$

Draw side $AB$ of $4$cm.

In a rhombus, all sides are equal and diagonals bisect the opposite angles

From $\left(1\right)$ we get, $\angle A={120}^o$

$⟹\angle B={60}^o$ ........... (Adjacent angles are supplementary)

Draw a side $AD$ from A of $4$cm such that $\angle BAD={120}^o$

Now, from $D$, draw side $DC=4$cm such that $\angle ADC={60}^o$

And then join $B-C$ such that $BC=4$cm and $\angle DCB={120}^o$.

At last we get a rhombus $ABCD$ with length of each side is $4$ cm and diagonals $AC$ and $BD$.

Hence, we can construct a rhombus with $AB=4cm$.