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.

Correct answer:

m = 3/2 s

Step-by-step explanation:

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

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