Answer:
Dimensions: 125 m x 250 m
Area: 31,250 m²
Step-by-step explanation:
Given information:
- Total amount of fencing = 500m
- Only 3 sides of the land need to be fenced
First, let us assume that the land is <u>rectangular</u> in shape.
Let = length of the side opposite the river
Let = length of the other 2 sides of the land
Therefore, we can create two equations from the given information:
<u>Area of land</u>:
<u>Perimeter of fence</u>:
Rearrange the equation for the perimeter of the fence to make y the subject:
Substitute this into the equation for Area:
To find the value of x that will make the area a <em>maximum</em>, <u>differentiate</u> A with respect to x:
Set it to zero and solve for x:
Substitute the found value of x into the original equation for the perimeter and solve for y:
Therefore, the dimensions that will give Christine the maximum area are:
125 m x 250 m (where 250 m is the side opposite the river)
The maximum area is: