Question

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

area is half into base into height

Answer 2

Answer:

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

Step-by-step explanation:

ABC be an isosceles triangle whose congruent sides are AC = BC = 13 cm and AB = 10 cm.

Now, mark all points by taking origin as A (0,0) in first Quadrant of Cartesian Co-ordinate system.

Then, A= (0,0) and B = (10,0)

Now, I isosceles triangle, and CE is median passing through centroid D

Therefore, AE = BE = 5 cm

⇒ E = (5,0)

In triangle ACE,

By Pythagoras Theorem,

EC² = AC² - AE²

⇒ EC² = 13² - 5²

⇒ EC = 12 cm

⇒ C = (5,12)

Centroid of triangle ABC,

$C=(\frac{(x_1 + x_2 + x_3)}{3} ,\frac{(y_1+y_2+y_3)}{3})\\\\\implies C =(\frac{(0+ 10+ 5)}{3} ,\frac{(0+0+12)}{3})\\\\\implies C = (\frac{15}{3} ,\frac{12}{3})\\\\\implies C = (5, 4)$

Now, By distance formula,

Distance between vertex opposite the base and centroid is :

$CD =\sqrt{(5-5)^2+(12-4)^2}\\\\\implies CD=8\thinspace{ cm}$

Hence, Distance between the vertex opposite the base and the centroid is 8 cm.