She wants to create a rectangular area of 1,600 square feet for her pet and can afford to purchase 160 feet of fence. In two or more complete sentences, explain the algebraic model, calculations and reasoning necessary to determine the dimensions of the rectangular area.

Answer: x = 40 and y = 40

Step-by-step explanation:

We can write the equation for the area as: x*y = 1600

We can write the equation for the perimeter as: 2x + 2y = 160

An easy way to solve a question like this is to graph both equations on a graphing calculator, if you don't have one on you you can use Desmos

Graph both: y = 1600/x

and

y = 80 - x

Turns out you get x = 40 and y = 40