Trapezoid thirds

The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment.

Result

x = (Correct answer is: ) OK

Solution:

S1=xh/2 S2=(ax)h S1=S2 xh/2=(ax)h x=2a2x 3x=2a x=AE=2/3 aS_{1}=xh/2 \ \\ S_{2}=(a-x)h \ \\ S_{1}=S_{2} \ \\ xh/2=(a-x)h \ \\ x=2a - 2x \ \\ 3x=2a \ \\ x=|AE|=2/3 \ a



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Dr Math
AE = 2/3 AB

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