Question

Бісектриса трикутника ділить сторону на відрізки, різниця яких 2 см. Знайдіть периметр трикутника, якщо дві інші його сторони дорівнюють 6 см і 10 см.

Answer 1

Биссектриса делит сторону пропорционально сторонам
обозначим через х один из отрезков, на которые биссектрис а делит противолежащую сторону. тогда вторая часть по условию х+2
x/(x+2)=6/10
10x=6x+12
4x=12
x=3
третья сторона (3+2)+3=8
Р=10+6+8=24

Answer 2

Bisector of a Triangle and Perimeter Calculation

The bisector of a triangle divides one of its sides into two segments, the difference of which is 2 cm. In this case, we are given that the other two sides of the triangle are 6 cm and 10 cm. We need to find the perimeter of the triangle.

To solve this problem, we can use the concept of the angle bisector theorem. According to this theorem, the angle bisector of a triangle divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

Let's assume that the bisector divides the side of length 6 cm into two segments, one of length x cm and the other of length (6 - x) cm. Since the difference between these two segments is 2 cm, we can set up the following equation:

x - (6 - x) = 2

Simplifying the equation, we get:

2x - 6 = 2

Adding 6 to both sides, we have:

2x = 8

Dividing both sides by 2, we find:

x = 4

Therefore, one segment of the bisected side is 4 cm, and the other segment is (6 - 4) = 2 cm.

Now, we can calculate the perimeter of the triangle by adding the lengths of all three sides:

Perimeter = 6 cm + 10 cm + 2 cm = 18 cm

So, the perimeter of the triangle is 18 cm.