Question

Центр вписаного у рівнобедрений трикутник кола ділить його висоту проведену до основи на відрізки 12 і 20 починаючи від основи. обчислити периметр трикутника

Answer 1

S=p*r

r=12

S=1/2a*h=1\2a*(12+20)=16a

16a=12P

p=4/3a 

 

Answer 2

Given Information

We are given that the center of the inscribed circle of a triangle divides the altitude drawn to the base into segments of length 12 and 20, starting from the base.

Approach

To find the perimeter of the triangle, we need to determine the lengths of its sides. We can use the given information about the inscribed circle to find the lengths of the segments of the base and the altitude. Then, we can apply the Pythagorean theorem to find the lengths of the other two sides of the triangle. Finally, we can calculate the perimeter by summing up the lengths of all three sides.

Solution

Let's denote the lengths of the segments of the base as x and y. According to the given information, we have x = 12 and y = 20.

To find the lengths of the other two sides of the triangle, we can use the fact that the center of the inscribed circle divides the altitude into segments of length 12 and 20. Let's denote the length of the altitude as h.

Using the Pythagorean theorem, we can write the following equation: h^2 = x * y

Substituting the given values, we have: h^2 = 12 * 20

Simplifying, we get: h^2 = 240

Taking the square root of both sides, we find: h = √240

Now, we can use the lengths of the base segments and the altitude to calculate the lengths of the other two sides of the triangle. Let's denote the lengths of these sides as a and b.

Using the Pythagorean theorem again, we can write the following equations: a^2 = x^2 + h^2 b^2 = y^2 + h^2

Substituting the given values, we have: a^2 = 12^2 + (√240)^2 b^2 = 20^2 + (√240)^2

Simplifying, we get: a^2 = 144 + 240 b^2 = 400 + 240

Calculating the values, we find: a^2 = 384 b^2 = 640

Taking the square root of both sides, we find: a = √384 b = √640

Finally, we can calculate the perimeter of the triangle by summing up the lengths of all three sides: Perimeter = x + y + a + b

Substituting the given values, we have: Perimeter = 12 + 20 + √384 + √640

Calculating the value, we find: Perimeter ≈ 12 + 20 + 19.60 + 25.30

Therefore, the approximate perimeter of the triangle is ≈ 76.90.

Answer

The approximate perimeter of the triangle is ≈ 76.90.