In the parallelogram ABCD, the besictrix of the angles B and D intersect the sides Ad and BC at points M and K

univerkov | August 22, 2021 | education

In the parallelogram ABCD, the besictrix of the angles B and D intersect the sides Ad and BC at points M and K, respectively, so that MD = 5cm, KС = 7cm. Find the perimeter ABCD.

Let us use the property of the bisector of a parallelogram, according to which, the bisector cuts off an isosceles triangle from the parallelogram.

Therefore, CK = CD, a AB = AM.

Since in a parallelogram the opposite sides are equal, AB = AM = CD = KC = 7 cm.

Since AM = KС, then ВK = MD = 5 cm.

Then AD = BC = 5 + 7 = 12 cm.

Find the perimeter of the parallelogram.

P = AB + BC + CD + AD = 5 + 12 + 5 + 12 = 34 cm.

Answer: P = 34 cm.

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