What is

What is the circumference of an isosceles trapezoid with an area of 106.75 cm²? The lengths of the sides are in the ratio of 1:3:2:1, and the bases are 6.1 cm apart.

Correct answer:

o =  49 cm

Step-by-step explanation:

$$\begin{gathered} S=106.75{\text{cm}}^2 \\ v=6.1\text{cm} \\ a=3x \\ c=2x \\ b=d=1x \\ S=(a+c)/2\cdot v \\ a+c=2\cdot S/v \\ 5\cdot x=2\cdot S/v \\ 5\cdot x=2\cdot 106.75/6.1 \\ 5x=35 \\ x=\frac{35}{5}=7 \\ x=7 \\ a=3\cdot x=3\cdot 7=21\text{cm} \\ c=2\cdot x=2\cdot 7=14\text{cm} \\ b=x=7\text{cm} \\ d=x=7\text{cm} \\ o=a+b+c+d=21+7+14+7=49\text{cm} \end{gathered}$$

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