Question

If G is the centroid of an equilateral triangle ABC e of side 5 cm then the length of AG is

Answer 1

G is centroid

AB is 5cm

so AG IS half of AB and

AG Is equal to 2.5

Answer 2

Answer:

AG = 5/√3 cm

Step-by-step explanation:

If G is the centroid of an equilateral triangle ABC e of side 5 cm then the length of AG is

As G is centroid of triangle

=> Area of ΔABG = (1/3) Area of ΔABC

Area of ΔABC = (√3 / 4) * 5² = 25√3/4

=> Area of ΔABG = 25/(4√3)

ABC is an equilateral triangle so Median is also perpendicular

let say GD is perpendicular to BC

Area of ΔABG = (1/2)AB * DG = (1/2) 5 * DG

comparing both

(1/2) 5 * DG =  25/(4√3)

=> DG = 5/(2√3)  cm

in Δ AGD

AG² = AD² + DG²

AD = AB/2 = 5/2

=> AG² = (5/2)² + (5/(2√3))²

=> AG² = 25/4  + 25/12

=> AG² = 100/12

=> AG² = 25/3

=> AG = 5/√3

Hence AG = 5/√3 cm