Given information: The gardener has 680ft of fencing on three sides of the garden.
Calculation:
Consider L as the length of the garden and B as the breadth of the rectangle.
Use the formula of the perimeter of rectangle and given figure.
The perimeter of the garden would be .
Therefore, the length of the garden can be find as,
The area of the rectangle is
Now find the area of the rectangular garden the formula of the area of the rectangle.
Compare the equation with the equation .
It can be seen that the above equation is the quadratic equation. The graph of the quadratic equation is the parabola.
The vertex of the parabola determines the maximum and minimum points of the parabola.
If the coefficient of is positive then the vertex is the minimum point and if the the coefficient of is negative then the vertex is the maximum point
The coefficient of is negative for the equation .
Therefore, the vertex of the equation leads to greatest area of the rectangular garden.
The vertex of the equation where the value of and .
In the equation , the value of for the maximum area can be find as,
Find the value of .
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