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?
Sure! Let's go through the steps to set up the scenario for fencing a rectangle in your yard for your pet.
1. Choose the amount of area you want to fence in for your pet. Let's say you want to enclose an area of 1000 sq. ft.
2. Choose a relationship between the length and the width of the rectangle. Let's say the relationship is L = W + 20, meaning the length is 20 more than the width.
3. Create a quadratic equation using the choices made in steps 1 and 2. Since the area is chosen as 1000 sq. ft and L = W + 20, the equation becomes A = L * W = (W + 20) * W = W^2 + 20W. So, the quadratic equation is 1000 = W^2 + 20W.
4. Solve the quadratic equation for the width (W) either by factoring or using the quadratic formula.
5. Substitute the value of W found in step 4 into the equation L = W + 20 to find the length (L) of the rectangle.
6. Calculate the perimeter (P) of the rectangle using the formula P = 2L + 2W.
7. Finally, summarize the meaning of your calculations in the context of your pet scenario. For example, you can say that to enclose an area of 1000 sq. ft for your pet, you would need to fence in a rectangle with dimensions of length L and width W. The length is 20 more than the width, and the perimeter of the fenced-in area would be P units. This ensures that your pet has enough space to roam safely within the fenced area.
Remember, these steps are just a guideline to help you set up the scenario and solve the problem. You can adjust the values and relationships based on your own preferences and requirements.