In the parallelogram ABCD, the bisectors of angles B and D intersect the sides AD and BC at points M

univerkov | August 16, 2021 | education

In the parallelogram ABCD, the bisectors of angles B and D intersect the sides AD and BC at points M and K, respectively, so that MD = 5cm, KC = 7cm. find the perimeter ABCD.

1. The bisector DK of the parallelogram ABCD separates the triangle DCК from it, which is isosceles (according to the properties of the parallelogram).

Therefore, СK = CD = 7 cm.

2. The bisector BM of the parallelogram ABCD separates the triangle BAM from it, which is isosceles (according to the properties of the parallelogram).

Therefore, AB = AM.

3. AB = CD = 7 cm. AM = 7 cm.

4. AD = AM + DM = 7 + 5 = 12 cm.

5. The total length of the sides of the parallelogram (perimeter) is 2 (AB + AD) = 2 (7 + 12) = 38 cm.

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