The bisector of one of the corners of the parallelogram divides it into 2 parts, the difference between the perimeters is 10 cm. Find the perimeter of the parallelogram if the sides of the parallelogram are 4: 9.
Let the length of the side AB = 4 * X cm, then the length of the side AD = 9 * X cm.
Since ABCD is a parallelogram, then CD = AB = 4 * X cm, BC = AD = 9 * X cm.
AK is the bisector of angle A, then it cuts off the isosceles triangle ABK in which VK = AB = 4 * X cm.
Let’s define the perimeters of triangle ABK and quadrilateral AKСD.
Ravk = (AB + BK + AK) = 8 * X + AK.
Raxd = (KС + CD + AD + AK) = (5 * X + 4 * X + 9 * X + AK) = 18 * X + AK.
By condition, Raksd – Ravk = 10.
18 * X + AK – 8 * X – AK = 10.
10 * X = 10.
X = 10/10 = 1.
Then AB = 4 cm, AD = 9 cm.
Ravsd = 2 * (AB + AD) = 2 * 13 = 26 cm.
Answer: The perimeter of the parallelogram is 26 cm.
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