Question

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

Answer 1

Answer:

Part a) $G.F=13\ units$

Part b) $A.F=39\ units$

Part c) $F.C=22\ units$

Part d) $G.B=24\ units$

Part e) $D.B=36\ units$

Step-by-step explanation:

we know that

The 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

$A.G=\frac{2}{3} A.F$

we have

$A.G=26\ units$

substitute

$26=\frac{2}{3} A.F$

Solve for A.F.

$A.F=26(3)/2$

$A.F=39\ units$

step 2

Find the value of G.F.

$G.F=\frac{1}{3} A.F$

substitute the value of A.F

$G.F=\frac{1}{3} (39)=13\ units$

step 3

Find 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 triangle

so

$F.C=\frac{1}{2}B.C$

we have

$B.C=44\ units$

substitute

$F.C=\frac{1}{2}(44)$

$F.C=22\ units$

step 4

Find the value of D.B.

$D.G=\frac{1}{3} D.B$

we have

$D.G=12\ units$

substitute

$12=\frac{1}{3} D.B$

$D.B=12(3)=36\ units$

step 5

Find the value of G.B

$G.B=\frac{2}{3} D.B$

substitute the value of D.B.

$G.B=\frac{2}{3} (36)$

$G.B=24\ units$