The acute angle of the parallelogram is 30 degrees and the sides of the parallelogram are 4cm and 6cm.

The acute angle of the parallelogram is 30 degrees and the sides of the parallelogram are 4cm and 6cm. Perpendiculars are drawn from vertices B and D. Find the perimeter of the resulting rectangle.

In a right-angled triangle ABH, the leg BH lies opposite an angle of 30, then BH = AB / 2 = 4/2 = 2 cm.

By the Pythagorean theorem, we determine the length of the leg AH.

AH ^ 2 = AB ^ 2 – BH ^ 2 = 16 – 4 = 12.

AH = 2 * √3 cm.

Then the length of the segment DН = АD – АН = 6 – 2 * √3 cm.

Quadrilateral BMDH is a rectangle, then its perimeter is equal to: Rvmdn = 2 * (BH + DH) = 2 * (2 + 6 – 2 * √3) = 4 * (4 – √3) cm.

Answer: The perimeter of the rectangle is 4 * (4 – √3) cm.