Question

19
ABC is an equilateral triangle of side 12 cm. If G is the controid, find
the length of AG.
OD 37​

Answer 1

Answer:

Step-by-step explanation:

ABC is equilateral triangle

AB = BC = CA = 12 cm

G is the centroid of equilateral triangle

Construct AD which is perpendicular to BC as a base where AD divides both BC into two equal parts,

So BD = DC = 12/2 = 6 cm

Now, as per above statement D is the midpoint of Base BC then AD is a median for the base BC of triangle ABC,

Let triangle ADC and apply Pythagorean theorem

AD² + DC² = AC²

AD² = AC² - DC²

AD =  

AD = √(12² - 6²)

AD = √( 144 - 36)

AD = √108

AD = 6√3 cm

Now AD is a median and centroid divide the median into 2:3

So,

AG = 4√3 cm is answer

Answer 2

Answer:

AB = AC = BC = 12 cm ∴ BD = BC/2 = 12/2 = 6 cm In right angled triangle ABD, AB2 = BD2 + AD2 AD2 = AB2 – BD2 = 122 – 62 = 144 – 36 = 108 AD = √108 AD = 6√3 We know that AG = 2/3 AD = 12/2 × 6√3 = 4√3Read more on Sarthaks.com - https://www.sarthaks.com/759195/sides-of-equilateral-triangle-abc-is-12-cm-each-if-g-is-its-centroid-then-find-ag