The perimeter of parallelogram ABCD is 40. The bisector of angle ABC intersects side AD

univerkov | June 22, 2021 | education

The perimeter of parallelogram ABCD is 40. The bisector of angle ABC intersects side AD at point M. Find the perimeter of BMDC if BAD is 60 degrees and side AB = 8.

In a parallelogram, the sum of adjacent angles is 180, then the angle ABC = (180 – 60) = 120.

ВM is the bisector of the angle ABC, then the angle ABM = 120/2 = 60, and then the triangle ABM is equilateral, AB = BM = AM = 8 cm.

Let the length DM = X cm, then AD = BC = (8 + X) cm.

The perimeter of the parallelogram is: P = 2 * (AB + AD) = 40 cm.

2 * (8 + 8 + X) = 40.

X = 20 – 16 = 4 cm.

Then BC = 8 + 4 = 12 cm.

Let’s define the perimeter of the BMDC quadrangle.

Rvmds = (BC + CD + DM + BM) = (12 + 8 + 4 + 8) = 32 cm.

Answer: the perimeter is 32 cm.

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