posted by jim on .
0. Tell your classmates about your pet to set up the scenario for fencing a rectangle in your yard.
1. You MUST start by choosing an amount of area that you want to fence in for your pet and this MUST be stated first. What amount of area are you enclosing with a fence for your pet? (A = 1000 sq. ft or A = 200 sq. yards or A = 500 sq. meters or...)
2. Next, you MUST choose a relationship between the length and the width of the rectangle (e.g., L = 2W - 3 or W = L - 10 or L = W + 20 or ...)
3. Next, you MUST create a quadratic equation from the choices you made in 1 and 2 above. For example, if area was chosen to be A = 1000 sq. ft. and L = W + 20, then A = L*W = (W + 20)*W = W^2 + 20*W, so 1000 = W^2 + 20*W, and that is a quadratic equation.
NOTE: I could also write a quadratic equation here in terms of L as: since L = W + 20, then W = L - 20, so A = L*W = L*(L - 20) = L^2 - 20*L, and then replacing A by 1000, the quadratic equation will be, 1000 = L^2 - 20*L. Either way will give exactly the same length and width for the rectangular fenced-in area.
4. Next, using either factoring or the quadratic formula you MUST SOLVE this quadratic equation for W (or L if your quadratic equation is in terms of L).
5. Next, you MUST solve for the other side's dimension using L = W + 20. If the quadratic equation is in terms of W, then replace W by the solution to the quadratic equation; if the quadratic equation is in terms of L, then replace L in L = W + 20 and solve for W.
6. Next, you MUST show the calculations for the perimeter, P = 2*L + 2*W.
7. Finally, you MUST summarize the meanings of your calculations in the context of your stated pet scenario.
What area, length and width are you choosing?