please me to answer this question.because i will pass this coming monday march 21,2011.fin the diameter of three circle inscribed in a triangle. whose base is 50 cm.
To find the diameter of three circles inscribed in a triangle, you will first need to determine the inradius of the triangle. The inradius is the radius of a circle that is tangent to all three sides of the triangle.
To find the inradius, you can use the formula:
Inradius = Area / Semiperimeter
1. Calculate the area of the triangle:
To calculate the area, you'll need the height of the triangle. Since the triangle is isosceles (the base is 50 cm), you can draw an altitude (perpendicular line) from the top vertex to the base, creating two right triangles.
Since the base is 50 cm and the triangle is isosceles, you can divide the base by 2 to find each half: 50 cm / 2 = 25 cm.
Now, to calculate the height, you'll need to use the Pythagorean theorem:
height^2 = (25 cm)^2 - x^2 (where 'x' represents half the length of the base)
height^2 = 625 cm^2 - x^2
Since the altitude divides the triangle into two congruent right triangles, each has the same height as the whole triangle. So you can solve for the height (h) using the equation above.
2. Calculate the area of the triangle:
Area of the triangle = (base * height) / 2 = (50 cm * h) / 2
3. Calculate the semiperimeter of the triangle:
Semiperimeter = (a + b + c) / 2
Since the triangle is isosceles, two sides are equal. Thus, the length of each of the two equal sides is (50 cm / 2) = 25 cm. Let's call this length 'a' for convenience.
Semiperimeter = (a + a + b) / 2 = (25 cm + 25 cm + b) / 2 = (50 cm + b) / 2
Now substitute the values into the formula for the inradius:
Inradius = Area / Semiperimeter
Inradius = [(50 cm * h) / 2] / [(50 cm + b) / 2]
Simplify: Inradius = (50 cm * h) / (50 cm + b)
4. Calculate the diameter of the inscribed circles:
Since the inradius is the radius of the circle, the diameter will be twice the inradius.
Diameter = 2 * Inradius
Now, you can calculate the diameter of each of the three inscribed circles using the formula above.