Question

an isosceles triangle length of the congruent side is 13 cm and its base is 10 cm find the distance between the vertex opposite the base and the centroid

Answer 1

Distance between the vertex opposite the base and the centroid is 8 cm

Step-by-step explanation:

See the figure attached

In an Isosceles triangle the median is ⊥ to base

∴ AD is ⊥ to BC

∴ BD = 5 cm

AB = 13 cm

So in right angle triangle Δ ABD

BD² + AD² = AB²

5² + AD² = 13²

25 + AD² = 169

AD² = 169 - 25

AD² = 144

AD = 12 cm

Now centroid G divides AG and GD in ratio 2:1

Now , AG + GD = 12

$\frac{AG}{GD} = \frac{2}{1}$

GD = $\frac{AG}{2}$

$AG +\frac{AG}{2} = 12$

$\frac{3 AG}{2} = 12$

$AG = \frac{12 * 2}{3}$

$AG =\frac{24}{3}$

AG = 8cm

So the Distance between the vertex opposite the base and the centroid is 8 cm