The bisector of angle A divides the side BC of the parallelogram ABCD in half. Find the perimeter
| September 10, 2021 | education
The bisector of angle A divides the side BC of the parallelogram ABCD in half. Find the perimeter of the parallelogram eslm side AB = 5 cm
The bisector AK of the parallelogram ABCD forms an isosceles triangle ABK at the lateral side AB, since the angles at the base of the AK triangle are equal. Then AB = ВK = 5 cm.
By condition, AK divides the BC side of the parallelogram in half, then ВC = СK = 5 cm.
BC = ВK + SK = 5 + 5 = 10 cm.
In a parallelogram, the lengths of the opposite sides are equal, then AB = CD = 5 cm, BC = AD = 10 cm.
Let’s calculate the perimeter of the parallelogram.
Ravsd = 2 * (AB + BC) = 2 * (5 + 10) = 30 cm.
Answer: The perimeter of the parallelogram is 40 cm.
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