Question

Бісектриса трикутника ділить сторону на вiдрiаки, рiз ниця яких 2 см. Знайдіть периметр трикутника, якщо двi iншi сторони дорівнюють 9 см і 15 см. МАКСИМАЛЬНО СРОЧНО!!!!! ДАЮ 25 БАЛОВ!!!​

Answer 1

Ответ:

Объяснение:

Фото

Answer 2

Bisector of a Triangle and Perimeter Calculation

The bisector of a triangle divides a side into two segments that have a difference in length of 2 cm. To find the perimeter of the triangle, we need to determine the lengths of the three sides.

Let's denote the lengths of the two given sides as a = 9 cm and b = 15 cm. The bisector divides one of the sides into two segments, with a difference in length of 2 cm. Let's call these segments x and y.

According to the given information, we have the following equation:

x - y = 2 cm.

To find the values of x and y, we can set up a system of equations using the properties of the bisector. Let's solve this system:

Equation 1: x + y = a (since the bisector divides side 'a' into segments 'x' and 'y'). Equation 2: x - y = 2 cm.

To solve this system, we can add the two equations together:

(x + y) + (x - y) = a + 2 cm.

Simplifying the equation, we get:

2x = a + 2 cm.

Substituting the value of a = 9 cm, we have:

2x = 9 cm + 2 cm.

Simplifying further, we get:

2x = 11 cm.

Dividing both sides by 2, we find:

x = 5.5 cm.

Now, we can substitute the value of x into Equation 1 to find the value of y:

5.5 cm + y = 9 cm.

Subtracting 5.5 cm from both sides, we get:

y = 9 cm - 5.5 cm.

Simplifying further, we find:

y = 3.5 cm.

Therefore, the lengths of the segments are x = 5.5 cm and y = 3.5 cm.

To calculate the perimeter of the triangle, we add the lengths of all three sides:

Perimeter = a + b + c.

Substituting the given values, we have:

Perimeter = 9 cm + 15 cm + c.

To find the length of the third side, c, we can use the fact that the bisector divides it into segments of length x = 5.5 cm and y = 3.5 cm. Therefore, we have:

c = x + y.

Substituting the values, we find:

c = 5.5 cm + 3.5 cm.

Simplifying, we get:

c = 9 cm.

Now, we can substitute the value of c into the perimeter equation:

Perimeter = 9 cm + 15 cm + 9 cm.

Simplifying further, we find:

Perimeter = 33 cm.

Therefore, the perimeter of the triangle is 33 cm.

I hope this helps! Let me know if you have any further questions.