Question

Бісектриса кута А паралелограма ABCD ділить сторо ну ВС на два відрізки ВК і КС так, що BK : КС = 2:4 Знайдіть сторони паралелограма, якщо його периметр дорівнює 48 см.​

Answer 1

Відповідь: 6 см, 6 см , 18 см, 18 см.

Пояснення:

фото.

Answer 2

#### Bisector of Angle A in Parallelogram ABCD In a parallelogram ABCD, the bisector of angle A divides side BC into two segments, BK and KS, such that BK:KS = 2:4. We need to find the lengths of the sides of the parallelogram if its perimeter is 48 cm. To solve this problem, we can use the properties of a parallelogram and the given information about the bisector of angle A. #### Properties of a Parallelogram In a parallelogram, opposite sides are equal in length. Therefore, we can conclude that side AB is equal in length to side CD, and side BC is equal in length to side AD. Let's denote the length of side AB as x cm. Then, the length of side CD is also x cm. #### Using the Bisector of Angle A Since the bisector of angle A divides side BC into two segments, BK and KS, such that BK:KS = 2:4, we can determine the lengths of BK and KS. Let's denote the length of BK as 2y cm and the length of KS as 4y cm. According to the given information, BK:KS = 2:4. This means that the ratio of the lengths of BK and KS is 2:4. Using this ratio, we can write the following equation: 2y / 4y = 2 / 4 Simplifying the equation, we get: 1 / 2 = 1 / 2 This equation is true, which means that the given ratio is valid. #### Finding the Perimeter of the Parallelogram The perimeter of a parallelogram is the sum of the lengths of all its sides. In this case, the perimeter of the parallelogram ABCD is given as 48 cm. Since opposite sides of a parallelogram are equal in length, we can express the perimeter in terms of the lengths of sides AB and BC: Perimeter = 2(AB + BC) Substituting the values we found earlier, we have: 48 = 2(x + 2y + 4y) 48 = 2(x + 6y) 24 = x + 6y #### Solving the Equations We now have two equations: x = 24 - 6y (Equation 1) x = CD = AB (Equation 2) We can substitute Equation 1 into Equation 2 to find the value of x: 24 - 6y = x Substituting this value back into Equation 1, we have: 24 - 6y = 24 - 6y This equation is true, which means that the values of x and y can be any real numbers. #### Conclusion In conclusion, the lengths of the sides of the parallelogram ABCD can be any real numbers, as long as the perimeter is 48 cm and the ratio of BK to KS is 2:4. The specific values of the sides cannot be determined without additional information. Please let me know if there is anything else I can help you with!