Question

Fråga 5 20 poäng A farmer wants to plant a small rectangular plot of ornamental blue corn. He has enough fencing material to enclose a space with a perimeter of 144 feet. He wants to know the dimensions of the largest rectangle that can be enclosed with 144 feet of fence. To help find them, he graphed the following equation. Area = x (72 - x) What are the dimensions of the largest area the farmer can enclose with 144 feet of fence?

Answer 1

The maximum dimensions is a square of sides 36 ft by 36 ft;

The maximum area is 1,296 ft^2

Here, we want to know the diemensions of the largest area the farmer can enclose within the perimeter

Mathematically, the greatest dimension that can maximize the area of the plot is the shape being a square

In other words, we need the diemnsions of both sides to be equal so as to get the area

If the dimensions are equal, we can say the length and width are represented by x

The length is thus as follows;

`\begin{gathered} 4\text{ }*\text{ x = 144} \\ 4x\text{ = 144} \\ \text{ x = 144/4} \\ x\text{ = 36 ft} \end{gathered}`

The greatest possible or the maximum area is thus;

`36*36=1,296ft^2`