cat 2021 Question 11

Question

Let ABCD be a parallelogram. The lengths of the side AD and the diagonal AC are 10 cm and 20 cm, respectively. If the angle ∠ADC is equal to 30° then the area of the parallelogram, in sq. cm, is

Accepted Answer

Applying cosine rule in triangle ACD:

$100 + X^2 - 2 imes 10 imes X \cos 30 = 400$

$X^2 - 10X\sqrt{3} - 300 = 0$

Solving, we get $X = \frac{10\sqrt{3} + 10\sqrt{15}}{2}$

Hence, area = $10X\sin 30 = \frac{\left(10\sqrt{3} + 10\sqrt{15} ight)10}{2 \cdot 2}$

$= 25(\sqrt{3} + \sqrt{15})$

Question 11.

Question Explanation