CENTROID is the term used to describe the point where the three medians of a triangle intersect.
Centroid is the center of gravity of the triangle. It is one of the triangle's point of concurrency. Aside from "center of gravity", it is also known as "center of mass" and "barycenter".
Centroids are always inside the triangle. Since, the centroid is where three medians intersect, each median divides the triangle into two smaller triangles of equal area. The centroid is exactly two-thirds the way along each median.
Other types of triangle centers aside from Centroids are:
1) incenter
2) circumcenter
3) orthocenter
The formula for the Pythagorean theorem is,
The sum of angles of a triangle is 180°.
48 +(6x -28) +2x = 180
8x +20 = 180
8x = 160
x = 20
∠B = (6x -28)° = (6*20 -28)° = 92°
∠C = 2x° = 40°
___
x = 20
∠B = 92°
∠C = 40°
The perimeter is:
P = 2x + 2y = 80
The area is:
A = x * y
The area as a function of a variable is:
A (x) = x * (40-x)
Rewriting we have:
A (x) = 40x-x ^ 2
We derive the function:
A '(x) = 40-2x
We equal zero and clear x:
40-2x = 0
2x = 40
x = 40/2
x = 20 feet
The other dimension is:
y = 40 - x
y = 40 - 20
y = 20 feet
The area will be:
A = x * y
A = 20 * 20
A = 400 feet ^ 2
Answer:
The dimensions are:
x = 20 feet
y = 20 feet
The area is:
A = 400 feet ^ 2
