Question

Биссектриса угла А паралелограма ABCD делит сторону CD в отношении 1:3 к вершине С, найти стороны, если периметр 84см. Желательно развёрнутый ответ

Answer 1

Обозначим биссектрису АК. ДК:СК=1:3.
Биссектриса в параллелограмме отсекает от противоположной стороны отрезок равный меньшей стороне параллелограмма, значит АД=ДК.
Пусть АД=ВС=х, тогда СД=х+х/3=4х/3.
Р=2(АД+СД)=2(х+4х/3)=14х/3=84,
14х=252,
х=18.
АД=ВС=18 см, АВ=СД=4·18/3=24 см - это ответ.

Answer 2

I have searched the web for your question and found some relevant results. Here is a summary of what I found:

- The problem is about finding the sides of a parallelogram ABCD, given that the bisector of angle A divides the side CD in the ratio 1:3 to the vertex C, and the perimeter is 84 cm. - One possible solution is based on the fact that the bisector of an angle in a parallelogram cuts off a segment from the opposite side equal to the smaller side of the parallelogram. Therefore, if we let AD = BC = x, then CD = x + x/3 = 4x/3. The perimeter is then 2(AD + CD) = 2(x + 4x/3) = 14x/3 = 84, which implies that x = 18. Hence, AD = BC = 18 cm, and AB = CD = 4x/3 = 24 cm. This is the answer. - Another possible solution is based on the fact that the angles 1 and 2 are equal, since AK is the bisector of angle A, and the angles 1 and 3 are equal as alternate interior angles between parallel lines BC and AD and the transversal AK. Therefore, the angles 2 and 3 are equal and the triangle ABK is isosceles. This means that AB = BK = 8 cm. Then, AB = CD = 8 cm, and BC = BK + KC = 12 cm, and BC = AD = 12 cm. The perimeter is then 2(AB + BC) = 2(8 + 12) = 40 cm. This is another answer.

I hope this helps you understand the problem and the solutions. If you have any further questions, please feel free to ask.