Question

A wire of length $50cm$ is to be bent in the form of a parallelogram of area $50c{m}^2$. If the angle between the adjacent sides is ${30}^{\circ }$, then the dimensions of the parallelogram are

• A. $15cm,10cm$
• B. $13cm,12cm$
• C. $20cm,5cm$
• D. $17cm,8cm$

Answer 1

Answer: (C)

$20cm,5cm$

Area of parallelogram with two adjacent sides $a$ and $b$ is $=ab\sin \theta$, where $\theta$ is the angle between the two sides.

Using the values given in the question,
$50=ab\sin {30}^{\circ }=ab\times \frac{1}{2}$
$\Rightarrow ab=100...\left(1\right)$
Perimeter of parallelogram $=2a+2b=50$ (perimeter will be same as the length of original wire which was bent to get the parallelogram)

$\Rightarrow a+b=25...\left(2\right)$
Eliminating $a$ from $\left(1\right)$ and $\left(2\right)$ we get, $b^2-25b+100=0$
$b=20cm,5cm$