Question

72 The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Find the length of the segment determined by the points of intersection between the line and the other two sides of the triangle.

Answer 1

18√2

Explanation:

The smaller triangle sharing a vertex with the larger one is similar and half the area. That means its linear dimensions are √(1/2) = (√2)/2 times those of the larger triangle.

The line segment of interest has length ...

36 × (√2)/2 = 18√2

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The ratio of area of similar figures is the square of the ratio of their linear dimensions. Thus the ratio of linear dimensions is the square root of the ratio of area.