Answer to Question #102928 in Geometry for jehan

Question

Area of parallelogram is 2019 square unite. Leanth and width of it is integer. then, what is the minimum perimeter value for it?

Answer 1

Solution. The parallelogram area can be calculated using the formula

$$S=aH_a=bH_b=ab\times sin\alpha$$

where a, b are sides parallelogram; α is the angle between the sides of the parallelogram; Ha and Hb are parallelogram heights. The perimeter will be minimal if the sides of the parallelogram are perpendicular. Therefore

$$S=ab$$

By factoring the number 2019, we get

$$2019=3\times673$$

Numbers 3 and 673 are prime.

As result the minimum perimeter value  is equal to

$$P=2(3+673)=1352$$

Answer. 1352.