In an equilateral triangle, a line through its centroid parallel to the base contains an interior point P . Let h be the distance of P from the base, and h 1 , h 2 its distances from the other sid

Question

In an equilateral triangle, a line through its centroid parallel to the base contains an interior point P . Let h be the distance of P from the base, and h 1 ​ , h 2 ​ its distances from the other sides. Which mean of h 1 ​ , h 2 ​ equals h ?

TestHub · Accepted Answer

If the triangle's side is a and altitude H , area decomposition gives H = h + h 1 ​ + h 2 ​ . Because the line through the centroid is at distance h = H /3 from the base, h 1 ​ + h 2 ​ = 2 h .

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