The bisector of angle A of the parallelogram ABCD intersects the side BC at point K.
| September 6, 2021 | education
The bisector of angle A of the parallelogram ABCD intersects the side BC at point K. Find the perimeter of the parallelogram if BK = 12, CK = 16.
The bisector AK is a secant for the opposite sides of this parallelogram, since the opposite sides of the parallelogram are parallel. Hence the angle BKA = KAD – as internal versatile angles. In turn, the angle BAK = BKA since AK is a bisector. Triangle ABK – isosceles, we have AB = BK = 12 cm – as lateral sides. Side CD = AB = 12 cm – as opposite sides of the parallelogram, BC = BK + KС = 12 + 16 = 28 (cm). AD = BC = 28 cm – as opposite sides of a parallelogram. We find the perimeter of the parallelogram P = 2AB + 2BC = 2 * 12 + 2 * 28 = 24 + 56 = 80 (cm).
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