Question

G is centroid of the triangle ABC, where AB, BC and CA are 7 cm, 24 cm and 25 cm respectively, then BG is:

Options

• `6 1/3` cm

• `8 1/3` cm

• `5 1/2` cm

• `4 1/6` cm

Answer 1

`8 1/3` cm

Explanation:

Here, AB² + BC² = 72 + 24²

= 49 + 576

= 625

⇒ AB² + BC² = 25² = AC²

BD = `b/3 = 24/3` = 8

BE = `h/3 = 7/3` = DG

∴ BG = `sqrt(BD^2 + DG^2)`

= `sqrt(8^2 + (7/3)^2)`

= `sqrt(64 + 49/9)`

= `sqrt((576 + 49)/9)`

= `sqrt(625/9)`

= `25/3`

= `8 1/3` cm.