In parallelogram ABCD, the bisector of angle B intersects AD at point M, and the extension of CD

univerkov | September 4, 2021 | education

In parallelogram ABCD, the bisector of angle B intersects AD at point M, and the extension of CD at point N. Find the perimeter of triangle BCN if AB = 6, DN = 4, BM = 9

The diagonal BN of the angle ABC forms an isosceles triangle ABM, in which AM = AB = 6 cm.

Triangles ABM and DMN are similar in two angles, then:

AВ / DN = ВM / MN.

MN = DN * VM / AB = 4 * 9/6 = 6 cm.

AB / AM = DN / DM.

DM = AM * DN / AB = 6 * 4/6 = 4 cm.

AD = BC = AM + DM = 6 + 4 = 10 cm.

CN = CD + DN = 6 + 4 = 10 cm.

ВN = ВМ + MN = 9 + 6 = 16 cm.

Then Рвсn = BN + СN + BC = 15 + 10 + 10 = 35 cm.

Answer: The perimeter of the BCN triangle is 35 cm.

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