Parallelogram ABCD. The bisector of an obtuse angle B divides the AD
| February 6, 2021 | education
Parallelogram ABCD. The bisector of an obtuse angle B divides the AD side into two segments (AK is 4 cm more than KD) P = 64 cm find all sides.
1. KD = AK – 4 cm (according to the problem statement).
2. The bisector of the parallelogram ВK separates the isosceles triangle AВK from it, whose sides AB and AK are equal.
3. AD = AK + KD.
We replace in this expression AK by AB, KD by (AB – 4):
AD = AB + AB – 4 = 2AB – 4 cm.
4. R parallelogram = 2 (AB + AD) = 64 cm.
AB + AD = 32 cm.
5. We replace in this expression AD for (2AB – 4):
AB + 2AB – 4 = 32 cm.
3AB – 4 = 32 cm.
3AB = 36 cm.
AB = 12 cm.
AD = 32 – AB = 32 – 12 = 20 cm.
Answer: AB = CD = 12 cm, AD = BC = 20 cm.
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