SOLUTION: 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

Algebra ->  Triangles -> SOLUTION: 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      Log On


   



Question 1133131: 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 by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Call the larger triangle ABC
Then the smaller triangle CDE is similar to ABC (all angles are equal, AAA).
AB is the side that is 36, and we wish to find DE, the side corresponding to AB

Area_CDE = Area_ABC - Area_CDE --> Area_ABC / Area_CDE = 2

Let x=length of DE
Ratio of areas = (ratio of sides)^2
+2+=+%2836%2Fx%29%5E2+
+2+=+1296%2Fx%5E2+
++x%5E2+=+1296%2F2+=+648+
+x+=+sqrt%28648%29+ or approx. +highlight%28+25.45584+%29+