The bisector of the angle A of the parallelogram ABCD intersects the side BC at the point P¸ BP = 4 cm and PC = 10 cm.

univerkov | December 12, 2020 | education

The bisector of the angle A of the parallelogram ABCD intersects the side BC at the point P¸ BP = 4 cm and PC = 10 cm. Calculate the perimeter of the parallelogram ABCD.

Parallelogram perimeter ABCD = 2AB + 2BC. Let’s find these sides.
BP + PC = BC. BC = 4 + 10 = 14.
Angle DAP = BPA = BAP, as these are criss-cross corners. It follows that the triangle BAP is isosceles. Hence BP = AB = 4
Perimeter = 2 * 4 + 2 * 14 = 36

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