If G is the centroid of triangle ACE, AG = 26, BC = 44, DG = 12, find each missing measure

Accepted Solution

Answer:Part a) [tex]G.F=13\ units[/tex]Part b) [tex]A.F=39\ units[/tex]Part c) [tex]F.C=22\ units[/tex]Part d) [tex]G.B=24\ units[/tex]Part e) [tex]D.B=36\ units[/tex]Step-by-step explanation:we know thatThe centroid of a triangle is the point where the three median.s coincide.The centroid is located two thirds of the distance from any vertex of the triangle.step 1 Find the value of A.F.we know that[tex]A.G=\frac{2}{3} A.F[/tex]we have[tex]A.G=26\ units[/tex]substitute[tex]26=\frac{2}{3} A.F[/tex]Solve for A.F.[tex]A.F=26(3)/2[/tex][tex]A.F=39\ units[/tex]step 2Find the value of G.F.[tex]G.F=\frac{1}{3} A.F[/tex]substitute the value of A.F[tex]G.F=\frac{1}{3} (39)=13\ units[/tex]step 3Find the value of F.C. Remember that a median of a triangle is a line segment from one vertex to the mid-point on the opposite side of the triangleso[tex]F.C=\frac{1}{2}B.C[/tex]we have[tex]B.C=44\ units[/tex]substitute[tex]F.C=\frac{1}{2}(44)[/tex][tex]F.C=22\ units[/tex]step 4Find the value of D.B. [tex]D.G=\frac{1}{3} D.B[/tex]we have[tex]D.G=12\ units[/tex]substitute[tex]12=\frac{1}{3} D.B[/tex][tex]D.B=12(3)=36\ units[/tex]step 5Find the value of G.B[tex]G.B=\frac{2}{3} D.B[/tex]substitute the value of D.B.[tex]G.B=\frac{2}{3} (36)[/tex][tex]G.B=24\ units[/tex]