Assuming that the attached file is the lake which you are mentioning in the question.
The perimeter is the distance around the lake, we need to set up an equation based on the statement "When Amanda jogged twice around the lake she jogged a distance of 2,700 meters" as below:
[tex] 2(Perimeter \; of\; the\; lake) =2700\\ \\ 2(x+140+x+x+250+x+x+3x)=2700\\ Group \; Like\; Terms\\ \\ 2(x+x+x+x+x+3x+140+250)=2700\\ Combine \; Like\; Terms\\ \\ 2(8x+390)=2700\\ Distribute\; 2\; in\; left\; side\; of\; the\; equation\\ \\ 16x+780=2700\\ Subtract \; 780\; on\; both\; sides\\ \\ 16x+780-780=2700-780\\ Combine \; like\; terms\\\\16x=1920 \\ Divide\; 16 \; on\; both\; sides\\ \\ \frac{16x}{16}=\frac{1920}{16}\\ Simplify\; fraction\; on\; both\; sides\\ \\ x=120 [/tex]
Conclusion:
The value of x is 120 meters
