use the given information to write a function

Question

A family just bought a puppy and wants to fence in part of the yard. The fenced-in area is a
rectangular section of the yard that is separate from all other structures on the property. The
family has purchased 70 feet of fencing. What function models the area of the pen?

Answer 1

Did you omit a diagram or other information? We have nearly nothing to work with. All we know is that the pen is rectangular, and therefore has a perimeter of:
P = 2L + 2W

and an area of...

A = L*W

Since we know that the perimeter is 70, we can clarify...
70 = 2L + 2W and you can solve for one variable, such as L:
-2W -2W by subtracting the 2W first...
70 - 2W = 2L and then dividing by 2:
2 2 2

35 - W = L And substitute into the area formula:
A = L * W
A = (35 - W) * W
A = 35W - W2

Note that you could do it all in reverse, solving for W instead and getting the same pattern with "L".