in an isosceles triangle, length of the congruent sides is 13 cm and base is 10 cm .Find the distance between the vertex opposite the base and the centroid
Answers
Thus, s = 36/2 = 18cm.
Area of triangle = [18(18–13)(18–13)(18–10)}^0.5 = [18*5*5*8]^0.5 = 60 sq cm.
Altitude of the triangle = 60*2/10 = 12 cm.
Since the centroid is two thirds of the way from the vertex to any base, the answer to your question is 8 cm.
The distance between the vertex opposite the base and the centroid is 8 cm.
Given
In an isosceles triangle, ABC it has sides and base.
Where, AB = AC = 13 cm
BC = 10 cm
AM is the median on BC
P is the centroid on median BC.
BM = CM = 1/2 BC = 1/2×10 = 5 cm
Using, Apollonius theorem,
In ΔABC, M is the mid point of BC.
13² + 13² = 2AM² + 2(5)²
169 + 169 = 2AM² + 2(25)
338 = 2AM² + 50
2AM² = 338 - 50
2AM² = 288
AM² = 288 / 2 = 144
AM = 12 cm
"P" is the centroid which divides the median in the ratio of 2 : 1
AP : PM = 2 : 1
AP = 2 PM
AM = AP + PM
AM = AP + AP/2
= 3AP/2
AP = 2/3 AM
= 2/3 × 12
AP = 8 cm
Therefore, The distance between the vertex opposite the base and the centroid is 8 cm.
To learn more...
1. brainly.in/question/3655994
2. brainly.in/question/4089643