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: )

Solution:

$$\begin{gathered} S_1=xh\mathrm{/}2 \\ {S}_2=(a-x)h \\ {S}_1=S_2 \\ xh\mathrm{/}2=(a-x)h \\ x=2a-2x \\ 3x=2a \\ x=\mathrm{\mid }AE\mathrm{\mid }=2\mathrm{/}3a \end{gathered}$$

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Dr Math

AE = 2/3 AB

3 years ago  Like

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