1) What radius of a circle is required to inscribe an equilateral triangle with an area of 15.588 in2 and an altitude of 5.196 in? (round to nearest tenth)
Accepted Solution
A:
we know that the distance from the centroid of the triangle to one of the vertices is the radius of the circle required to inscribe an equilateral triangle.
[distance centroid of the triangle to one of the vertices]=(2/3)*h h=the altitude of the equilateral triangle-----> 5.196 in so [distance centroid of the triangle to one of the vertices]=(2/3)*5.196 [distance centroid of the triangle to one of the vertices]=3.464 in----> 3.5 in
the radius is equal to the distance of the centroid of the triangle to one of the vertices hence the radius is 3.5 in