Question

g is the centroid of triangle abc. given fc=35, ag=42, bf=57 and dg=14, find t
ac= type your answer...
bg= type your answer...
gc= type your answer...
ae= type your answer...

Explanation:

Step1: Find length of AF

Since F is the midpoint of AC (centroid property), $AF = FC = 35$.

Step2: Calculate AC

Add AF and FC:
$AC = AF + FC = 35 + 35 = 70$

Step3: Find length of BG

Centroid divides median into 2:1, so $BG = 2 \times DG$.
$BG = 2 \times 14 = 28$

Step4: Calculate GC

Centroid divides median into 2:1, so $GC = \frac{2}{3} \times BF$.
$GC = \frac{2}{3} \times 57 = 38$

Step5: Find length of AE

E is the midpoint of BC, and centroid G divides AE into 2:1. First find total length of AE: $AE = \frac{3}{2} \times AG$.
$AE = \frac{3}{2} \times 42 = 63$

Answer:

$AC=70$
$BG=28$
$GC=38$
$AE=63$