Question

One side of a parallelogram is 12 cm and its area is $60c{m}^2$. If the angle between the adjacent sides is ${30}^0$, then its other side is

• A. $10$ cm
• B. $8$ cm
• C. $6$ cm
• D. $4$ cm

Answer 1

The correct option is A $10$ cm

Given that, in the parallelogram $ABCD$, $AD=12cm,\angle DAE={30}^o$ and $A\left(ABCD\right)=60c{m}^2$

Draw a line from $D$ perpendicular to $AB$ which intersects it at $E$.

Now, $△AED={90}^o$ is a right-angled triangle

$⟹\sin {30}^o=\frac{DE}{AD}$

$⟹\frac{1}{2}=\frac{DE}{12}$

$⟹DE=6cm$

$A\left(Parallelogram\right)=b\times h$

Now, we know that $A\left(ABCD\right)=AB\times DE$

$⟹60=AB\times 6$

$⟹AB=10cm$

Then the other side of a parallelogram is $10cm$.