Trapezoid 25

Trapezoid PART with AR||PT has (angle P=x) and (angle A=2x) . In addition, PA = AR = RT = s.
Find the length of the median of Trapezoid PART in terms of s.

Result

m = (Correct answer is: 3/2 s)

Step-by-step explanation:

$$\begin{gathered} x+2x+x+2x=360 \\ x=360\mathrm{/}(1+2+1+2)=60\text{ ° } \\ \cos x=z\mathrm{/}s \\ \cos 60\mathrm{°}={\displaystyle \frac{1}{2}}=z\mathrm{/}s \\ 1:2=z:s \\ z=0.5\cdot s \\ PT=2\cdot z+s=2\cdot 0.5\cdot s+s=s+s=2s \\ m={\displaystyle \frac{PT+AR}{2}} \\ m={\displaystyle \frac{2s+s}{2}} \\ m=3\mathrm{/}2s \end{gathered}$$

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