Area of triangle = 1/2 base x height
15.588 = 1/2 * base x 5.196
15.588 = base x 2.598
base = 15.588 / 2.598 = 6
equi center of triangle = 1/3*5.196 = 1.732
radius of circle = Sqrt(1.732^2 + 3^2) =
sqrt (2.999824 +9) =
sqrt(11.999824) = 3.464
rounded to nearest tenth = 3.5 inches
The radius of the circle required to inscribe an equilateral triangle with the given dimensions is; radius = 3.5 inches
Usually, when we inscribe an equilateral triangle in a circle, the distance from the centroid of that triangle to one of the vertices is;
Centroid distance to vertex = ²/₃h
Where h is the altitude of the triangle.
We are given altitude = 5.196 in
Thus;
Centroid distance to vertex = ²/₃(5.196)
⇒ 3.464 inches
Approximating to the nearest tenth gives;
Centroid distance to vertex = 3.5 inches
Now, the distance from centroid to vertex of the inscribed equilateral triangle is also the radius of the circle.
Thus; radius = 3.5 inches
Read more at; https://brainly.com/question/9854426
