In a triangle ABC, AD is the median, G is the centroid and AP is the altitude such that P lies between C and D. Given that GD = 2.5cm and AP=6cm, find DP.

Answer 1

In order to understand this problem it is essential to draw a figure.

As described triangle APD is a right triangle and the median AD is the hypotenuse.

Since the length of GD is 2.5, the length of AD is 7.5.; the length of AP (one leg of the right triangle) is given as 6..

Therefore, PD = sqrt(7.5^2 - 6^2)=sqrt(20.25)=4.5