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

August 31, 2021 | education

| **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.

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