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

Answer 1

Let's be a and b the sides of the rectangle.

1 Area is 1600 =a*b
2. Perimeter is 2(a+b)=160 ==>b=80-a

So,
1600=a*b=a*(80-a)==>80a-a²=1600
==> a²-80a+1600=0
==> (a-40)²=0
==>a=40 or a=-40 (to exclude since <0)
==>b=1600/40=40
The rectangle is a square of 40m of side.