Concept:Area of a parallelogram = product of adjacent sides × sine of the included angle. Perimeter = 2 × (sum of adjacent sides).
Explanation:Let AB and DA be adjacent sides. Given ∠ABC = 60°, so the angle between AB and DA is also 60°.
Area = AB × DA × sin 60° = AB × DA × (√3/2) = 7√3.
Thus, AB × DA = 14.
Only natural number factor pairs of 14 are (1,14) and (2,7). Because sides must be greater than 1 unit (Statement II), only (2,7) or (7,2) remain.
Perimeter = 2 × (2 + 7) = 18 units.
Statement-I says AB and DA are prime. The only prime pair with product 14 is (2,7). So Statement I alone gives the perimeter.
Statement-II says sides are natural numbers >1. The only such pair is (2,7). So Statement II alone also gives the perimeter.
Answer:Option B. The Question can be answered by using either Statement alone.