Question

A town planner is building a fountain in the middle of a triangular shaped park and will place the fountain at the centroid of the triangle.

A diagram of the triangular park shown by △ABD was used to determine the location of the fountain, which will be at point G. The longest median of the triangular park, AC¯¯¯¯¯, is 150 feet.

What is the distance from the corner of the park, at point A, to the fountain?

Enter your answer in the box.

Answer 1

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Answer:

100 ft

Explanation:

The centroid divides each median into parts in the ratio 2 : 1. The longest part is 2/(2+1) = 2/3 of the whole length of the median.

That is, AG = 2/3AC = (2/3)(150 ft) = 100 ft.