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Answer:
Step-by-step explanation:
Answer:
Dimensions: 150 m x 150 m
Area: 22,500m²
Step-by-step explanation:
Given information:
- Rectangular field
- Total amount of fencing = 600m
- All 4 sides of the field need to be fenced
Let = width of the field
Let = length of the field
Create two equations from the given information:
<u>Area of field</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 Tanya the maximum area are:
150 m x 150 m
The maximum area is: