Question

боковые стороны равнобедренного треугольника равны 5,основание 6.найти радиус вписанной окружности

Answer 1

 

 

 СD = 4. SABC=1/2(6*4) = 12 Воспользуемся формулой для вычисления радиуса.

 

S=1/2PR

 

12=1/2*16*R

R=12/8

R=1.5 

Answer 2

Given Information:

We are given that the two equal sides of an isosceles triangle are 5 units long, and the base is 6 units long. We need to find the radius of the inscribed circle.

Solution:

To find the radius of the inscribed circle in an isosceles triangle, we can use the formula:

radius = (area of the triangle) / (semiperimeter of the triangle)

The area of the triangle can be calculated using Heron's formula:

area = sqrt(s * (s - a) * (s - b) * (s - c))

where s is the semiperimeter of the triangle, and a, b, and c are the lengths of the sides of the triangle.

In this case, since the triangle is isosceles, we can simplify the formula further. Let's denote the equal sides as a and the base as b. The semiperimeter can be calculated as:

s = (2a + b) / 2

Substituting the values given in the problem, we have:

a = 5 (length of the equal sides) b = 6 (length of the base)

Calculating the semiperimeter:

s = (2 * 5 + 6) / 2 = 16 / 2 = 8

Now, we can calculate the area of the triangle:

area = sqrt(8 * (8 - 5) * (8 - 5) * (8 - 6)) = sqrt(8 * 3 * 3 * 2) = sqrt(144) = 12

Finally, we can calculate the radius of the inscribed circle:

radius = area / s = 12 / 8 = 1.5

Therefore, the radius of the inscribed circle in the given isosceles triangle is 1.5 units.

Answer:

The radius of the inscribed circle in the given isosceles triangle is 1.5 units.