Question

Знайдіть радіус кола вписаного в рівнобедрений трикутник з основою 48 см і бічною стороною 40см

Answer 1

SΔ=pΔ*r
pΔ=PΔ/2
PΔ=48+40+40, PΔ=128
pΔ=128/2, pΔ=64 см
SΔ=√(p*(p-a)*(p-b)*(p-c))
SΔ=√(64*(64-48)*(64-40)*(64-40))
SΔ=768 см²
768=64*r
r=768/64
r=12  см

Answer 2

Finding the Radius of the Inscribed Circle in an Isosceles Triangle

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

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

Let's calculate the radius using the given information:

- Base of the triangle (b) = 48 cm - Length of the side (a) = 40 cm

Calculating the Area of the Triangle

The area of an isosceles triangle can be calculated using the formula:

area = (base * height) / 2

In this case, the height of the triangle can be found using the Pythagorean theorem:

height = sqrt(a^2 - (b/2)^2)

Substituting the given values, we have:

height = sqrt(40^2 - (48/2)^2) = sqrt(1600 - 576) = sqrt(1024) = 32

Now, we can calculate the area of the triangle:

area = (48 * 32) / 2 = 768 cm^2

Calculating the Semiperimeter of the Triangle

The semiperimeter of a triangle is half the sum of its three sides. In this case, since the triangle is isosceles, two sides are equal, and one side is different.

The semiperimeter can be calculated as:

semiperimeter = (a + b + b) / 2 = (40 + 48 + 48) / 2 = 88 cm

Calculating the Radius of the Inscribed Circle

Now that we have the area of the triangle and the semiperimeter, we can calculate the radius of the inscribed circle:

radius = area / semiperimeter = 768 cm^2 / 88 cm = 8.73 cm

Therefore, the radius of the circle inscribed in the given isosceles triangle with a base of 48 cm and a side length of 40 cm is approximately 8.73 cm.

Please note that the calculations provided are based on the given information and formulas.