Question

1. In an isosceles triangle, length of the
congruent sides is 13 cm and its base is 10 cm.
Find the distance between the vertex opposite
the base and the centroid.​

Answer 1

Answer:

Step-by-step explanation:

Let ABC be an isosceles triangle, In which AB = AC = 13 cm

And BC = 10 cm

Let AM be median on BC such that

Let P be centroid on median BC

To Find : AP [Distance between vertex opposite the base and centroid]

We know, By Apollonius theorem

In ΔABC, if M is the midpoint of side BC, then AB2 + AC2 = 2AM2 + 2BM 2

Putting values, we get

(13)2 + (13)2 = 2AM2 + 2(5)2

⇒ 169 + 169 = 2AM2 + 50

⇒ 2AM2 = 288

⇒ AM2 = 144

⇒ AM = 12 cm

Let P be the centroid

As, Centroid divides median in a ratio 2 : 1

⇒ AP : PM = 2 : 1

⇒ AP = 2PM

Now, AM = AP + PM

AP = 8cm