Question

Tina is planning to fence in an area for her dog. 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.

Hint: Using variables for the side lengths of the rectangular area, set up an equation for the area and an equation for the perimeter.

Answer 1

If you do 20x80, you can easily get a perimeter below the 160 she can afford as well as the 1600sqf needed area. And it's a rectangle.

Answer 2

Let
a=length of the rectangle
and
b=width of the rectangle
Then,
the area =ab
and
the perimeter
p=2(a+b)
You can solve the equations for a and b

Answer 3

ab=1600
2(a+b)=160
a+b=80
b=80-a
a(80-a)=1600
\[80a-a^2=1600\]
\[a^2-80a+1600=0\]
\[a^2-40a-40a+1600=0\]
\[a^2-40a-40a+1600=0\]
a(a-40)-40(a-40)=0
\[a(a-40)-40(a-40)=0\]
\[(a-40)(a-40)=0\]
find a and then b