Assuming that the pathway is a rectangle, we use the equations: Area = Length x Width and Perimeter = 2L + 2W. We substitue the values, we have: 350 = LW and 90 = 2L + 2W. We get W in terms of L in the first equation: (350/L) = W. We use the value of W we got earlier to the 2nd equation to get the numerical value of L: 2L + 2(350/L) = 90 --> 2L + (700/L) = 90 --> We multiply both sides of equation L to get a quadratic equation: 2L^2 - 90L +700 =0 --> L = 10 and 35.
