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.Com
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) (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
or approx.
RELATED QUESTIONS
The area of a triangle is divided into 5 equal parts by line segments parallel to one... (answered by greenestamps)
The area of a triangle is divided into 6 equal parts by line segments parallel to one... (answered by greenestamps,ikleyn)
The area of a triangle is divided into 3 equal parts by line segments parallel to one... (answered by ikleyn)
The area of a triangle is divided into 6 equal parts by line segments parallel to one... (answered by greenestamps,ikleyn)
The area of a triangle is divided into 3 equal parts by line segments parallel to one... (answered by ikleyn)
Prove that a line that divides two sides of a triangle proportionally is parallel to the... (answered by ikleyn)
parallel lines and proportional parts of triangles
There is a triangle with a line that (answered by Fombitz)
Prove that a line parallel to one side of a triangle divides the other two sides... (answered by Edwin McCravy)
A theorem regarding proportional line segments states that if a line is parallel to one... (answered by lwsshak3)