Question

Бісектриса тупого кута паралелограма ділить йього сторону у відношені 1:3, рахуючи від вершини тупого кута , Периметр паралелограма дорівнює 84см, Знайдіть йтого сторони​

Answer 1

На одну сторону приходится 1 часть какого-то числа, на вторую 3 части какого-то числа. То есть предположительно отношение сторон 1/3 сократили на какое-то число и получили конечную дробь 1/3. Это число - k - коэффициент пропорциональности.

Пусть x = k.

КАК ПОНЯТЬ КОЭФФИЦИЕНТ ПРОПОРЦИОНАЛЬНОСТИ:

допустим у нас есть сторона 4см и 8 см. Отношение этих сторон равно 4/8. Дробь можно сократить на 4, получим 1/2. Число на которое мы сократили отношение сторон - коэффициент пропорциональности, который равен 4.

Answer 2

Bisector of an obtuse angle in a parallelogram

In order to find the length of the side of the parallelogram that is divided by the bisector of the obtuse angle in a ratio of 1:3, we need to use the given information about the perimeter of the parallelogram.

Let's assume that the length of the shorter segment of the divided side is "x" cm. According to the given ratio, the length of the longer segment would be "3x" cm.

Finding the perimeter of the parallelogram

The perimeter of a parallelogram is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 84 cm.

To find the length of the divided side, we need to consider that the divided side is counted twice in the perimeter calculation (once for each segment). So, the equation to find the perimeter is:

2x + 2(3x) = 84

Simplifying the equation:

2x + 6x = 84 8x = 84 x = 10.5

Finding the length of the divided side

Now that we have found the value of "x" to be 10.5 cm, we can find the length of the divided side by multiplying it by the ratio.

The length of the shorter segment of the divided side is "x" cm, which is 10.5 cm. The length of the longer segment of the divided side is "3x" cm, which is 3 * 10.5 = 31.5 cm.

Therefore, the length of the divided side of the parallelogram is 10.5 cm for the shorter segment and 31.5 cm for the longer segment.

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