SOLUTION: Looking for help to solve the following geometry problem. One side of a triangle is 18 cm. Inside the triangle, a segment is drawn parallel to the 18 cm side, forming a trapezoid w

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Question 937835: Looking for help to solve the following geometry problem. One side of a triangle is 18 cm. Inside the triangle, a segment is drawn parallel to the 18 cm side, forming a trapezoid whose area is 1/3 that of the original triangle. Find the length of this segment.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The segment splits the original triangle into two pieces:
a trapezoid and a smaller top triangle.
h%2FH is the scaling factor between the two triangles
%28h%2FH%29%5E2=2%2F3 because the area of the top triangle is
1-1%2F3=2%2F3 of the area of the original triangle.
%28h%2FH%29%5E2=2%2F3--->h%2FH=sqrt%282%2F3%29=about0.8165 (rounded)
x%2F18cm=sqrt%282%2F3%29=about0.8165 (rounded)
x=sqrt%282%2F3%29%2A%2818cm%29=about14.7cm (rounded)